Author | Title | |
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József Vass | ||
Andrijana Burazin | ||
Nancy Soontiens | ||
Amenda Chow | ||
Rasha Al Jamal | ||
Wentao Liu | | |
Minghua Lin | ||
Killian Miller |
Author | Title | |
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Rahul Rahul | ||
Ruibin Qin | ||
Dominique Brunet | ||
Yasunori Aoki | ||
Easwar Magesan | ||
Christopher Ferrie | ||
Dhanaraja Kasinathan | ||
Wai Man NG | ||
Matthew Johnston |
Author | Title | |
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Raluca Jessop | ||
Yufang Hao | ||
Mohamad Alwan | ||
Yanwei Wang | ||
Christopher Subich | ||
Timothy Rees | ||
Volodymyr Gerasik |
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Jun Liu |
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Kathleen Wilkie |
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Sean Speziale |
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Nataliya Portman |
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Rudy Gunawan | ||
Gibin George Powathil | ||
Matthew Calder |
Author | Title | |
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Gregory Mayer | ||
Cedric Beny | ||
Lijun Wang | ||
Kahrizsangi Ebrahimi | ||
Robert Martin |
Author | Title | |
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Shannon Kennedy | ||
Alexander Korobov | ||
Qing Wang | ||
Duncan Mowbray | ||
Donald Campbell |
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This collection contains a selection of the latest doctoral theses completed at the School of Mathematics. Please note this is not a comprehensive record.
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
Efficient monte carlo methods for bayesian state-space model inference , well-posedness of nonlinear schrödinger equations from deterministic and probabilistic viewpoints , applications and improvements of the adaptive large neighbourhood search , lᵖ boundary value problems for elliptic and parabolic operators , twistor theory and its applications in asymptotically flat spacetimes , theory and simulation of interacting particle systems and mckean-vlasov processes: the super measure class, ergodicity, and weak error , spencer cohomology, supersymmetry and the structure of killing superalgebras , higher triangulated categories and fourier-mukai transforms on abelian surfaces and threefolds , investigating computer aided assessment of mathematical proof by varying the format of students' answers and the structure of assessment design by stack , estimation and application of bayesian hawkes process models , novel statistical learning approaches for open banking-type data , statistical and machine learning approaches to genomic medicine , using markov chain monte carlo in vector generalized linear mixed models: with an application to integral projection models in ecology , symmetries of riemann surfaces and magnetic monopoles , kan extensions in probability theory , regression analysis for extreme value responses and covariates , categorical torelli theorems for fano threefolds , laplacians for structure recovery on directed and higher-order graphs , efficient interior point algorithms for large scale convex optimization problems , solving sampling and optimization problems via tamed langevin mcmc algorithms in the presence of super-linearities .
Yuying Liu | Nathan Kutz & Steven Brunton | |
Jianghong Shi | Eric Shea-Brown | |
Bobby Baraldi | Aleksandr Aravkin | |
Yu-Chen Cheng | Hong Qian | |
Kenan Li | Anne Greenbaum | |
Benjamin Liu | Mark Kot | |
Kelsey Maass | Aleksandr Aravkin | |
Megan Morrison | Nathan Kutz | |
Diya Sashidhar | Nathan Kutz | |
Lowell Thompson | Hong Qian | |
Xin Yang | Bernard Deconinck & Thomas Trogdon | |
Yang Zhou | Tim Leung | |
Matthew Farrell | Eric Shea-Brown | |
Andreas L. Freund | Antonio Ferrante | |
Yuan Gao | James Burke | |
Kelsey Marcinko | Mark Kot | |
Sean Santos | Chris Bretherton/Peter Caldwell | |
Brian de Silva | Nathan Kutz/Steven Brunton | |
Jeremy Upsal | Bernard Deconinck | |
Xin Yang | Bernard Deconinck/Tom Trogdon | |
Jize Zhang | Aleksandr Aravkin | |
Yang Zhou | Tim Leung | |
Weston D. Barger | Matthew Lorig | |
Kathleen P. Champion | Nathan Kutz | |
Samuel H. Rudy | Nathan Kutz/Steven Brunton | |
Peng Zheng | Aleksandr Aravkin | |
Tommaso Buvoli | Randall LeVeque | |
Krithika Manohar | Nathan Kutz/Steven Brunton | |
Jacob Price | Panos Stinis | |
Yue Wang | Hong Qian | |
Felix Xiaofeng Ye | Hong Qian | |
Kameron Decker Harris | Eric Shea-Brown | |
Benjamin Lansdell | Adrienne Fairhall | |
Yian Ma | | Hong Qian |
Susan C. Massey | Kristin Swanson | |
Scott Moe | Randall LeVeque | |
Donsub Rim | Randall LeVeque | |
Daniel Shapero | Randall LeVeque/Ian Joughin | |
Timothy B. Oleskiw | Eric Shea-Brown | |
Niket Thakkar | David Masiello | |
Benjamin Segal | Bernard Deconinck | |
Xing Fu | Nathan Kutz | |
Jakob Kotas | Archis Ghate | |
Bethany Lusch | Nathan Kutz | |
Syuzanna Sargsyan | Nathan Kutz | |
Mauricio del Razo Sarmina | Randall LeVeque/Hong Qian | |
Natasha A. Cayco Gajic | Eric Shea-Brown | |
Kathleen M. Curtius | Georg Luebeck | |
Mikala C. Johnson | Nathan Kutz | |
Pedro D. Maia | Nathan Kutz | |
Natalie E. Sheils | Bernard Deconinck | |
Olga Trichtchenko | Bernard Deconinck | |
Meng-Huo Chen | Anne Greenbaum | |
Yu Hu | Eric Shea-Brown | |
Jihwan Kim | Randall LeVeque | |
Guillaume Lajoie | Eric Shea-Brown | |
Jacob R. Grosek | Nathan Kutz | |
Christopher R. Jones | Christopher Bretherton | |
Grady I. Lemoine | Randall LeVeque | |
Russell C. Rockne | Kristin Swanson | |
Thomas D. Trogdon | Bernard Deconinck | |
Mingyuan Zhong | Emo Todorov | |
Ying Zhou | Mark Kot | |
Nicholas Cain | Eric Shea-Brown | |
Joshua Jacobs | Randall LeVeque/Pascale Lelong | |
Laura Matarajt Arbetman | Mark Kot/Ira Longini | |
Vishal Vasan | Bernard Deconinck | |
Matthew Williams | Nathan Kutz | |
Yun Zhang | James Burke | |
Jiansong Zhou | Ka Kit Tung | |
Lisa Bishop | Hong Qian | |
Jonathan Claridge | Randall LeVeque | |
Joshua Goldwyn | Eric Shea-Brown | |
Edwin Ding | Nathan Kutz | |
Woo Hyun Kim | Hong Qian | |
Eleftherios Kirkinis | Robert O'Malley | |
Christine Lind | Hong Qian | |
Kyle Mandli | Randall LeVeque | |
Peizhe Shi | Hong Qian | |
Kirsten Fagnan | Randall LeVeque | |
Minsun Kim | Archis Ghate | |
Eric MacHorro | Anne Greenbaum | |
Junya Uchida | Chris Bretherton | |
Christopher Curtis | Bernard Deconinck | |
Dean Gull | Hong Qian | |
Larry Jean | Georg Luebeck | |
David Ketcheson | Randall LeVeque | |
Michael Nivala | Bernard Deconinck | |
Katie Oliveras | Bernard Deconinck | |
Yiyi Shi | Hong Qian | |
Melissa Vellela | Hong Qian | |
Brandon Bale | Nathan Kutz | |
Miguel Gomez | Anne Greenbaum | |
Gunog Seo | Mark Kot | |
Jason Slemons | Loyce Adams | |
Jihyoun Jeon | Suresh Moolgavkar | |
Matthew Patterson | Bernard Deconinck | |
Santosh Srivastava | Maya Gupta | |
David George | Randall LeVeque | |
Eleftherios Gkioulekas | Ka Kit Tung | |
Rafael Meza | Suresh Moolgavkar | |
Damon Toth | Mark Kot | |
Edward Farnum | Nathan Kutz | |
William Heuett | Hong Qian | |
Rie Komuro | E. David Ford | |
Marica Pelanti | Randall LeVeque | |
Matthew Peters | Christopher Bretherton | |
David Williams | Robert O'Malley | |
Sarah Hewitt | Nathan Kutz | |
Viktoria Hsu | Hong Qian | |
Jan Medlock | Mark Kot | |
Timothy Reluga | Mark Kot | |
Kathleen Coughlin | Ka Kit Tung | |
Rebecca Crabb | Thomas Leschine | |
Steven Kusiak | John Sylvester | |
Derek Bale | Randall LeVeque | |
Eric Dolven | Harry Yeh | |
Long Lee | Randall LeVeque | |
Blessing Mudavanhu | Robert O'Malley | |
James Rossmanith | Randall LeVeque | |
Tiernan Fogarty | Randall LeVeque | |
Karl Knaub | Robert O'Malley | |
David Luke | James Burke | |
Arnold Kim | Akira Ishimaru | |
Mark Martin | Mark Kot | |
Benjamin Moskowitz | Christopher Bretherton | |
Dominik Obrist | Peter Schmid | |
Darryl Yong | Jirair Kevorkian | |
Donna Calhoun | Randall LeVeque | |
Kristin Swanson | James Murray | |
Trachette Jackson | James Murray | |
Patrick Nelson | James Murray | |
Eric Stollnitz | David Salesin | |
Christopher Thompson | Ka Kit Tung | |
David Salinger | Terry Rockafellar | |
Daphne Manoussaki | James Murray | |
Wendell Orlando | Ka Kit Tung | |
Louis Stern | Randall LeVeque | |
Rebecca Tyson | James Murray | |
Zhiyun Yang | Loyce Adams | |
Cynthia Young | Akira Ishimaru | |
Chaoming Zhang | Randall LeVeque | |
Julian Cook | James Murray | |
Ming Fang | Ka Kit Tung | |
Paul Kulesa | James Murray | |
Thomas Milac | Frederic Wan | |
Hugh Rand | Christopher Bretherton | |
Lei Wang | Jirair Kevorkian | |
Katrin White | James Murray | |
Margaret Brown | Ka Kit Tung | |
George Chen | Terry Rockafellar | |
Chonghua Gu | Frederic Wan | |
Jacques Laforgue | Robert O'Malley | |
Zhilin Li | Randall LeVeque | |
Kristyn Maschhoff | Loyce Adams | |
William Mell | George Kosaly | |
Mike Neubert | Mark Kot | |
David Stevens | Chris Bretherton | |
Mei Zhu | James Murray | |
Charles Mannix | Ka Kit Tung | |
Keh-Ming Shyue | Randall LeVeque | |
Yeng Bun | William Criminale | |
Kevin Gates | Loyce Adams | |
Jeffrey Greenough | James Riley | |
Steven Siems | Chris Bretherton | |
Ciyou Zhu | Terry Rockafellar | |
Scott Coble | Juris Vagners | |
Mark Pernarowski | Jirair Kevorkian | |
Ruoxin Zhang | Terry Rockafellar | |
Richard Beyer | Randall LeVeque | |
David Bosley | Jirair Kevorkian | |
Marie Lelong | James Riley | |
Joseph Manke | Loyce Adams | |
Maria Ong | Loyce Adams | |
Radhakrishnan Srinivasan | Jirair Kevorkian | |
Kraig Winters | James Riley | |
Philip Harrison | Juris Vagners | |
Angel Muleshkov | Chris Bretherton | |
Jun Yu | Jirair Kevorkian | |
Pierre Mourad | ||
Donald Owen | Carl Pearson | |
Jeffrey Cordova | ||
Jie Sun |
Emily Dautenhahn Thesis: Heat kernel estimates on glued spaces Advisor: Laurent Saloff-Coste First Position: Assistant Professor at Murray State University
Elena Hafner Thesis: Combinatorics of Vexillary Grothendieck Polynomials Advisor: Karola Meszaros First Position: NSF Postdoctoral Fellow,, at University of Washington
Sumun Iyer Thesis: Dynamics of non-locally compact topological groups Advisor: Slawomir Solecki First Position: NSF Postdoctoral Fellow at Carnegie Mellon University in Pittsburgh
Sebastian Junge Thesis: Applications of Transferring the Ramsey Property between Categories Advisor: Slawomir Solecki First Position: Lecturer at Texas State University
Nicki Magill Thesis: Infinite Staircases for Hirzebruch Surfaces Advisor: Tara Holm First Position: NSF Postdoctoral Fellow at UC Berkeley
Prairie Wentworth-Nice Thesis: Finite Groups, Polymatroids, and Error-Correcting Codes Advisor: Edward Swartz First Position: Postdoctoral Teaching Fellow at Johns Hopkins University
Fiona Young Thesis: Dissecting an Integer Polymatroid Advisor: Edward Swartz First Position: Pursuing her own start-up in the math education technology space
Kimoi Kemboi Thesis: Full exceptional collections of vector bundles on linear GIT quotients Advisor: Daniel Halpern-Leistner First Position: Postdoc at the Institution for Advanced Study and Princeton
Max Lipton Thesis: Dynamical Systems in Pure Mathematics Advisor: Steven Strogatz First Position: NSF Mathematical Sciences Postdoctoral Fellow at Massachusetts Institute of Technology
Elise McMahon Thesis: A simplicial set approach to computing the group homology of some orthogonal subgroups of the discrete group Advisor: Inna Zakharevich First Position: Senior Research Scientist at Two Six Technologies
Andrew Melchionna Thesis: Opinion Propagation and Sandpile Models Advisor: Lionel Levine First Position: Quantitative Researcher at Trexquant
Peter Uttenthal Thesis: Density of Selmer Ranks in Families of Even Galois Representations Advisor: Ravi Kumar Ramakrishna First Position: Visiting Assistant Professor at Cornell University
Liu Yun Thesis: Towers of Borel Fibrations and Generalized Quasi-Invariants Advisor: Yuri Berest First Position: Postdoc at Indiana University Bloomington
Romin Abdolahzadi Thesis: Anabelian model theory Advisor: Anil Nerode First Position: Quantitative Analyst, A.R.T. Advisors, LLC
Hannah Cairns Thesis: Abelian processes, and how they go to sleep Advisor: Lionel Levine First Position: Visiting Assistant Professor, Cornell University
Shiping Cao Thesis: Topics in scaling limits on some Sierpinski carpet type fractals Advisor: Robert Strichartz (Laurent Saloff-Coste in last semester) First Position: Postdoctoral Scholar, University of Washington
Andres Fernandes Herrero Thesis: On the boundedness of the moduli of logarithmic connections Advisor: Nicolas Templier First Position: Ritt Assistant Professor, Columbia University
Max Hallgren Thesis: Ricci Flow with a Lower Bound on Ricci Curvature Advisor: Xiaodong Cao First Position: NSF Postdoctoral Research Fellow, Rutgers University
Gautam Krishnan Thesis: Degenerate series representations for symplectic groups Advisor: Dan Barbasch First Position: Hill Assistant Professor, Rutgers University
Feng Liang Thesis: Mixing time and limit shapes of Abelian networks Advisor: Lionel Levine
David Mehrle Thesis: Commutative and Homological Algebra of Incomplete Tambara Functors Advisor: Inna Zakharevich First Position: Postdoctoral Scholar, University of Kentucky
Itamar Sales de Oliveira Thesis: A new approach to the Fourier extension problem for the paraboloid Advisor: Camil Muscalu First Position: Postdoctoral Researcher, Nantes Université
Brandon Shapiro Thesis: Shape Independent Category Theory Advisor: Inna Zakharevich First Position: Postdoctoral Fellow, Topos Institute
Ayah Almousa Thesis: Combinatorial characterizations of polarizations of powers of the graded maximal ideal Advisor: Irena Peeva First position: RTG Postdoctoral Fellow, University of Minnesota
Jose Bastidas Thesis: Species and hyperplane arrangements Advisor: Marcelo Aguiar First position: Postdoctoral Fellow, Université du Québec à Montréal
Zaoli Chen Thesis: Clustered Behaviors of Extreme Values Advisor: Gennady Samorodnitsky First Position: Postdoctoral Researcher, Department of and Statistics, University of Ottawa
Ivan Geffner Thesis: Implementing Mediators with Cheap Talk Advisor: Joe Halpern First Position: Postdoctoral Researcher, Technion – Israel Institute of Technology
Ryan McDermott Thesis: Phase Transitions and Near-Critical Phenomena in the Abelian Sandpile Model Advisor: Lionel Levine
Aleksandra Niepla Thesis: Iterated Fractional Integrals and Applications to Fourier Integrals with Rational Symbol Advisor: Camil Muscalu First Position: Visiting Assistant Professor, College of the Holy Cross
Dylan Peifer Thesis: Reinforcement Learning in Buchberger's Algorithm Advisor: Michael Stillman First Position: Quantitative Researcher, Susquehanna International Group
Rakvi Thesis: A Classification of Genus 0 Modular Curves with Rational Points Advisor: David Zywina First Position: Hans Rademacher Instructor, University of Pennsylvania
Ana Smaranda Sandu Thesis: Knowledge of counterfactuals Advisor: Anil Nerode First Position: Instructor in Science Laboratory, Computer Science Department, Wellesley College
Maru Sarazola Thesis: Constructing K-theory spectra from algebraic structures with a class of acyclic objects Advisor: Inna Zakharevich First Position: J.J. Sylvester Assistant Professor, Johns Hopkins University
Abigail Turner Thesis: L2 Minimal Algorithms Advisor: Steven Strogatz
Yuwen Wang Thesis: Long-jump random walks on finite groups Advisor: Laurent Saloff-Coste First Position: Postdoc, University of Innsbruck, Austria
Beihui Yuan Thesis: Applications of commutative algebra to spline theory and string theory Advisor: Michael Stillman First Position: Research Fellow, Swansea University
Elliot Cartee Thesis: Topics in Optimal Control and Game Theory Advisor: Alexander Vladimirsky First Position: L.E. Dickson Instructor, Department of , University of Chicago
Frederik de Keersmaeker Thesis: Displaceability in Symplectic Geometry Advisor: Tara Holm First Position: Consultant, Addestino Innovation Management
Lila Greco Thesis: Locally Markov Walks and Branching Processes Advisor: Lionel Levine First Position: Actuarial Assistant, Berkshire Hathaway Specialty Insurance
Benjamin Hoffman Thesis: Polytopes And Hamiltonian Geometry: Stacks, Toric Degenerations, And Partial Advisor: Reyer Sjamaar First Position: Teaching Associate, Department of , Cornell University
Daoji Huang Thesis: A Bruhat Atlas on the Wonderful Compactification of PS O(2 n )/ SO (2 n -1) and A Kazhdan-Lusztig Atlas on G/P Advisor: Allen Knutson First Position: Postdoctoral Associate, University of Minnesota
Pak-Hin Li Thesis: A Hopf Algebra from Preprojective Modules Advisor: Allen Knutson First position: Associate, Goldman Sachs
Anwesh Ray Thesis: Lifting Reducible Galois Representations Advisor: Ravi Ramakrishna First Position: Postdoctoral Fellowship, University of British Columbia
Avery St. Dizier Thesis: Combinatorics of Schubert Polynomials Advisor: Karola Meszaros First Position: Postdoctoral Fellowship, Department of , University of Illinois at Urbana-Champaign
Shihao Xiong Thesis: Forcing Axioms For Sigma-Closed Posets And Their Consequences Advisor: Justin Moore First Position: Algorithm Developer, Hudson River Trading
Swee Hong Chan Thesis: Nonhalting abelian networks Advisor: Lionel Levine First Position: Hedrick Adjunct Assistant Professor, UCLA
Joseph Gallagher Thesis: On conjectures related to character varieties of knots and Jones polynomials Advisor: Yuri Berest First Position: Data Scientist, Capital One
Jun Le Goh Thesis: Measuring the Relative Complexity of Mathematical Constructions and Theorems Advisor: Richard Shore First Position: Van Vleck Assistant Professor, University of Wisconsin-Madison
Qi Hou Thesis: Rough Hypoellipticity for Local Weak Solutions to the Heat Equation in Dirichlet Spaces Advisor: Laurent Saloff-Coste First Position: Visiting Assistant Professor, Department of , Cornell University
Jingbo Liu Thesis: Heat kernel estimate of the Schrodinger operator in uniform domains Advisor: Laurent Saloff-Coste First Position: Data Scientist, Jet.com
Ian Pendleton Thesis: The Fundamental Group, Homology, and Cohomology of Toric Origami 4-Manifolds Advisor: Tara Holm
Amin Saied Thesis: Stable representation theory of categories and applications to families of (bi)modules over symmetric groups Advisor: Martin Kassabov First Position: Data Scientist, Microsoft
Yujia Zhai Thesis: Study of bi-parameter flag paraproducts and bi-parameter stopping-time algorithms Advisor: Camil Muscalu First Position: Postdoctoral Associate, Université de Nantes
Tair Akhmejanov Thesis: Growth Diagrams from Polygons in the Affine Grassmannian Advisor: Allen Knutson First position: Arthur J. Krener Assistant Professor, University of California, Davis
James Barnes Thesis: The Theory of the Hyperarithmetic Degrees Advisor: Richard Shore First position: Visiting Lecturer, Wellesley College
Jeffrey Bergfalk Thesis: Dimensions of ordinals: set theory, homology theory, and the first omega alephs Advisor: Justin Moore Postdoctoral Associate, UNAM - National Autonomous University of Mexico
TaoRan Chen Thesis: The Inverse Deformation Problem Advisor: Ravi Ramakrishna
Sergio Da Silva Thesis: On the Gorensteinization of Schubert varieties via boundary divisors Advisor: Allen Knutson First position: Pacific Institute for the Mathematical Sciences (PIMS) postdoctoral fellowship, University of Manitoba
Eduard Einstein Thesis: Hierarchies for relatively hyperbolic compact special cube complexes Advisor: Jason Manning First position: Research Assistant Professor (Postdoc), University of Illinois, Chicago (UIC)
Balázs Elek Thesis: Toric surfaces with Kazhdan-Lusztig atlases Advisor: Allen Knutson First position: Postdoctoral Fellow, University of Toronto
Kelsey Houston-Edwards Thesis: Discrete Heat Kernel Estimates in Inner Uniform Domains Advisor: Laurent Saloff-Coste First position: Professor of Math and Science Communication, Olin College
My Huynh Thesis: The Gromov Width of Symplectic Cuts of Symplectic Manifolds. Advisor: Tara Holm First position: Applied Mathematician, Applied Research Associates Inc., Raleigh NC.
Hossein Lamei Ramandi Thesis: On the minimality of non-σ-scattered orders Advisor: Justin Moore First position: Postdoctoral Associate at UFT (University Toronto)
Christine McMeekin Thesis: A density of ramified primes Advisor: Ravi Ramakrishna First position: Researcher at Max Planck Institute
Aliaksandr Patotski Thesis: Derived characters of Lie representations and Chern-Simons forms Advisor: Yuri Berest First position: Data Scientist, Microsoft
Ahmad Rafiqi Thesis: On dilatations of surface automorphisms Advisor: John Hubbard First position: Postdoctoral Associate, Sao Palo, Brazil
Ying-Ying Tran Thesis: Computably enumerable boolean algebras Advisor: Anil Nerode First position: Quantitative Researcher
Drew Zemke Thesis: Surfaces in Three- and Four-Dimensional Topology Advisor: Jason Manning First position: Preceptor in , Harvard University
Heung Shan Theodore Hui Thesis: A Radical Characterization of Abelian Varieties Advisor: David Zywina First position: Quantitative Researcher, Eastmore Group
Daniel Miller Thesis: Counterexamples related to the Sato–Tate conjecture Advisor: Ravi Ramakrishna First position: Data Scientist, Microsoft
Lihai Qian Thesis: Rigidity on Einstein manifolds and shrinking Ricci solitons in high dimensions Advisor: Xiaodong Cao First position: Quantitative Associate, Wells Fargo
Valente Ramirez Garcia Luna Thesis: Quadratic vector fields on the complex plane: rigidity and analytic invariants Advisor: Yulij Ilyashenko First position: Lebesgue Post-doc Fellow, Institut de Recherche Mathématique de Rennes
Iian Smythe Thesis: Set theory in infinite-dimensional vector spaces Advisor: Justin Moore First position: Hill Assistant Professor at Rutgers, the State University of New Jersey
Zhexiu Tu Thesis: Topological representations of matroids and the cd-index Advisor: Edward Swartz First position: Visiting Professor - Centre College, Kentucky
Wai-kit Yeung Thesis: Representation homology and knot contact homology Advisor: Yuri Berest First position: Zorn postdoctoral fellow, Indiana University
Lucien Clavier Thesis: Non-affine horocycle orbit closures on strata of translation surfaces: new examples Advisor: John Smillie First position: Consultant in Capital Markets, Financial Risk at Deloitte Luxembourg
Voula Collins Thesis: Crystal branching for non-Levi subgroups and a puzzle formula for the equivariant cohomology of the cotangent bundle on projective space Advisor: Allen Knutson FIrst position: Postdoctoral Associate, University of Connecticut
Pok Wai Fong Thesis: Smoothness Properties of symbols, Calderón Commutators and Generalizations Advisor: Camil Muscalu First position: Quantitative researcher, Two Sigma
Tom Kern Thesis: Nonstandard models of the weak second order theory of one successor Advisor: Anil Nerode First position: Visiting Assistant Professor, Cornell University
Robert Kesler Thesis: Unbounded multilinear multipliers adapted to large subspaces and estimates for degenerate simplex operators Advisor: Camil Muscalu First position: Postdoctoral Associate, Georgia Institute of Technology
Yao Liu Thesis: Riesz Distributions Assiciated to Dunkl Operators Advisor: Yuri Berest First position: Visiting Assistant Professor, Cornell University
Scott Messick Thesis: Continuous atomata, compactness, and Young measures Advisor: Anil Nerode First position: Start-up
Aaron Palmer Thesis: Incompressibility and Global Injectivity in Second-Gradient Non-Linear Elasticity Advisor: Timothy J. Healey First position: Postdoctoral fellow, University of British Columbia
Kristen Pueschel Thesis: On Residual Properties of Groups and Dehn Functions for Mapping Tori of Right Angled Artin Groups Advisor: Timothy Riley First position: Postdoctoral Associate, University of Arkansas
Chenxi Wu Thesis: Translation surfaces: saddle connections, triangles, and covering constructions. Advisor: John Smillie First position: Postdoctoral Associate, Max Planck Institute of
David Belanger Thesis: Sets, Models, And Proofs: Topics In The Theory Of Recursive Functions Advisor: Richard A. Shore First position: Research Fellow, National University of Singapore
Cristina Benea Thesis: Vector-Valued Extensions for Singular Bilinear Operators and Applications Advisor: Camil Muscalu First position: University of Nantes, France
Kai Fong Ernest Chong Thesis: Face Vectors and Hilbert Functions Advisor: Edward Swartz First position: Research Scientist, Agency for Science, Technology and Research, Singapore
Laura Escobar Vega Thesis: Brick Varieties and Toric Matrix Schubert Varieties Advisor: Allen Knutson First position: J. L. Doob Research Assistant Professor at UIUC
Joeun Jung Thesis: Iterated trilinear fourier integrals with arbitrary symbols Advisor: Camil Muscalu First position: Researcher, PARC (PDE and Functional Analysis Research Center) of Seoul National University
Yasemin Kara Thesis: The laplacian on hyperbolic Riemann surfaces and Maass forms Advisor: John H. Hubbard Part Time Instructor, Faculty of Engineering and Natural Sciences, Bahcesehir University
Chor Hang Lam Thesis: Homological Stability Of Diffeomorphism Groups Of 3-Manifolds Advisor: Allen Hatcher
Yash Lodha Thesis: Finiteness Properties And Piecewise Projective Homeomorphisms Advisor: Justin Moore and Timothy Riley First position: Postdoctoral fellow at Ecole Polytechnique Federale de Lausanne in Switzerland
Radoslav Zlatev Thesis: Examples of Implicitization of Hypersurfaces through Syzygies Advisor: Michael E. Stillman First position: Associate, Credit Strats, Goldman Sachs
Margarita Amchislavska Thesis: The geometry of generalized Lamplighter groups Advisor: Timothy Riley First position: Department of Defense
Hyungryul Baik Thesis: Laminations on the circle and hyperbolic geometry Advisor: John H. Hubbard First position: Postdoctoral Associate, Bonn University
Adam Bjorndahl Thesis: Language-based games Advisor: Anil Nerode and Joseph Halpern First position: Tenure Track Professor, Carnegie Mellon University Department of Philosophy
Youssef El Fassy Fihry Thesis: Graded Cherednik Algebra And Quasi-Invariant Differential Forms Advisor: Yuri Berest First position: Software Developer, Microsoft
Chikwong Fok Thesis: The Real K-theory of compact Lie groups Advisor: Reyer Sjamaar First position: Postdoctoral fellow in the National Center for Theoretical Sciences, Taiwan
Kathryn Lindsey Thesis: Families Of Dynamical Systems Associated To Translation Surfaces Advisor: John Smillie First position: Postdoctoral Associate, University of Chicago
Andrew Marshall Thesis: On configuration spaces of graphs Advisor: Allan Hatcher First position: Visiting Assistant Professor, Cornell University
Robyn Miller Thesis: Symbolic Dynamics Of Billiard Flow In Isosceles Triangles Advisor: John Smillie First position: Postdoctoral Researcher at Mind Research Network
Diana Ojeda Aristizabal Thesis: Ramsey theory and the geometry of Banach spaces Advisor: Justin Moore First position: Postdoctoral Fellow, University of Toronto
Hung Tran Thesis: Aspects of the Ricci flow Advisor: Xiaodong Cao First position: Visiting Assistant Professor, University of California at Irvine
Baris Ugurcan Thesis: LPLP-Estimates And Polyharmonic Boundary Value Problems On The Sierpinski Gasket And Gaussian Free Fields On High Dimensional Sierpinski Carpet Graphs Advisor: Robert S. Strichartz First position: Postdoctoral Fellowship, University of Western Ontario
Anna Bertiger Thesis: The Combinatorics and Geometry of the Orbits of the Symplectic Group on Flags in Complex Affine Space Advisor: Allen Knutson First position: University of Waterloo, Postdoctoral Fellow
Mariya Bessonov Thesis: Probabilistic Models for Population Dynamics Advisor: Richard Durrett First position: CUNY City Tech, Assistant Professor, Tenure Track
Igors Gorbovickis Thesis: Some Problems from Complex Dynamical Systems and Combinatorial Geometry Advisor: Yulij Ilyashenko First position: Postdoctoral Fellow, University of Toronto
Marisa Hughes Thesis: Quotients of Spheres by Linear Actions of Abelian Groups Advisor: Edward Swartz First position: Visiting Professor, Hamilton College
Kristine Jones Thesis: Generic Initial Ideals of Locally Cohen-Macaulay Space Curves Advisor: Michael E. Stillman First position: Software Developer, Microsoft
Shisen Luo Thesis: Hard Lefschetz Property of Hamiltonian GKM Manifolds Advisor: Tara Holm First position: Associate, Goldman Sachs
Peter Luthy Thesis: Bi-parameter Maximal Multilinear Operators Advisor: Camil Muscalu First position: Chauvenet Postdoctoral Lecturer at Washington University in St. Louis
Remus Radu Thesis: Topological models for hyperbolic and semi-parabolic complex Hénon maps Advisor: John H. Hubbard First position: Milnor Lecturer, Institute for Mathematical Sciences, Stony Brook University
Jenna Rajchgot Thesis: Compatibly Split Subvarieties of the Hilbert Scheme of Points in the Plane Advisor: Allen Knutson First position: Research member at the Mathematical Sciences Research Institute (fall 2012); postdoc at the University of Michigan
Raluca Tanase Thesis: Hénon maps, discrete groups and continuity of Julia sets Advisor: John H. Hubbard First position: Milnor Lecturer, Institute for Mathematical Sciences, Stony Brook University
Ka Yue Wong Thesis: Dixmier Algebras on Complex Classical Nilpotent Orbits and their Representation Theories Advisor: Dan M. Barbasch First position: Postdoctoral fellow at Hong Kong University of Science and Technology
Tianyi Zheng Thesis: Random walks on some classes of solvable groups Advisor: Laurent Saloff-Coste First position: Postdoctoral Associate, Stanford University
Juan Alonso Thesis: Graphs of Free Groups and their Measure Equivalence Advisor: Karen Vogtmann First position: Postdoc at Uruguay University
Jason Anema Thesis: Counting Spanning Trees on Fractal Graphs Advisor: Robert S. Strichartz First position: Visiting assistant professor of mathematics at Cornell University
Saúl Blanco Rodríguez Thesis: Shortest Path Poset of Bruhat Intervals and the Completecd-Index Advisor: Louis Billera First position: Visiting assistant professor of mathematics at DePaul University
Fatima Mahmood Thesis: Jacobi Structures and Differential Forms on Contact Quotients Advisor: Reyer Sjamaar First position: Visiting assistant professor at University of Rochester
Philipp Meerkamp Thesis: Singular Hopf Bifurcation Advisor: John M. Guckenheimer First position: Financial software engineer at Bloomberg LP
Milena Pabiniak Thesis: Hamiltonian Torus Actions in Equivariant Cohomology and Symplectic Topology Advisor: Tara Holm First position: Postdoctoral associate at the University of Toronto
Peter Samuelson Thesis: Kauffman Bracket Skein Modules and the Quantum Torus Advisor: Yuri Berest First position: Postdoctoral associate at the University of Toronto
Mihai Bailesteanu Thesis: The Heat Equation under the Ricci Flow Advisor: Xiaodong Cao First position: Visiting assistant professor at the University of Rochester
Owen Baker Thesis: The Jacobian Map on Outer Space Advisor: Karen Vogtmann First position: Postdoctoral fellow at McMaster University
Jennifer Biermann Thesis: Free Resolutions of Monomial Ideals Advisor: Irena Peeva First position: Postdoctoral fellow at Lakehead University
Mingzhong Cai Thesis: Elements of Classical Recursion Theory: Degree-Theoretic Properties and Combinatorial Properties Advisor: Richard A. Shore First position: Van Vleck visiting assistant professor at the University of Wisconsin at Madison
Ri-Xiang Chen Thesis: Hilbert Functions and Free Resolutions Advisor: Irena Peeva First position: Instructor at Shantou University in Guangdong, China
Denise Dawson Thesis: Complete Reducibility in Euclidean Twin Buildings Advisor: Kenneth S. Brown First position: Assistant professor of mathematics at Charleston Southern University
George Khachatryan Thesis: Derived Representation Schemes and Non-commutative Geometry Advisor: Yuri Berest First position: Reasoning Mind
Samuel Kolins Thesis: Face Vectors of Subdivision of Balls Advisor: Edward Swartz First position: Assistant professor at Lebanon Valley College
Victor Kostyuk Thesis: Outer Space for Two-Dimensional RAAGs and Fixed Point Sets of Finite Subgroups Advisor: Karen Vogtmann First position: Knowledge engineering at Reasoning Mind
Ho Hon Leung Thesis: K-Theory of Weight Varieties and Divided Difference Operators in Equivariant KK-Theory Advisor: Reyer Sjamaar First position: Assistant professor at the Canadian University of Dubai
Benjamin Lundell Thesis: Selmer Groups and Ranks of Hecke Rings Advisor: Ravi Ramakrishna First position: Acting assistant professor at the University of Washington
Eyvindur Ari Palsson Thesis: Lp Estimates for a Singular Integral Operator Motivated by Calderón’s Second Commutator Advisor: Camil Muscalu First position: Visiting assistant professor at the University of Rochester
Paul Shafer Thesis: On the Complexity of Mathematical Problems: Medvedev Degrees and Reverse Advisor: Richard A. Shore First position: Lecturer at Appalachian State University
Michelle Snider Thesis: Affine Patches on Positroid Varieties and Affine Pipe Dreams Advisor: Allen Knutson First position: Government consulting job in Maryland
Santi Tasena Thesis: Heat Kernel Analysis on Weighted Dirichlet Spaces Advisor: Laurent Saloff-Coste First position: Lecturer professor at Chiang Mai University, Thailand
Russ Thompson Thesis: Random Walks and Subgroup Geometry Advisor: Laurent Saloff-Coste First position: Postdoctoral fellow at the Mathematical Sciences Research Institute
Gwyneth Whieldon Thesis: Betti Numbers of Stanley-Reisner Ideals Advisor: Michael E. Stillman First position: Assistant professor of mathematics at Hood College
Andrew Cameron Thesis: Estimates for Solutions of Elliptic Partial Differential Equations with Explicit Constants and Aspects of the Finite Element Method for Second-Order Equations Advisor: Alfred H. Schatz First position: Adjunct instructor of mathematics at Tompkins Cortland Community College
Timothy Goldberg Thesis: Hamiltonian Actions in Integral Kähler and Generalized Complex Geometry Advisor: Reyer Sjamaar First position: Visiting assistant professor of mathematics at Lenoir-Rhyne University
Gregory Muller Thesis: The Projective Geometry of Differential Operators Advisor: Yuri Berest First position: Assistant professor at Louisiana State University
Matthew Noonan Thesis: Geometric Backlund transofrmation in homogeneous spaces Advisor: John H. Hubbard
Sergio Pulido Niño Thesis: Financial Markets with Short Sales Prohibition Advisor: Philip E. Protter First position: Postdoctoral associate in applied probability and finance at Carnegie Mellon University
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Main areas of research activity are algebra, including group theory, semigroup theory, lattice theory, and computational group theory, and analysis, including fractal geometry, multifractal analysis, complex dynamical systems, Kleinian groups, and diophantine approximations.
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Assouad-type dimensions and the local geometry of fractal sets , separability properties of semigroups and algebras , groups defined by language theoretic classes , rearrangement groups of connected spaces , modern computational methods for finitely presented monoids .
Columbia University | |
Department of Mathematics | |
Recent Doctoral Theses | |
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Here is the complete list of all doctoral dissertations granted by the School of Math, which dates back to 1965. Included below are also all masters theses produced by our students since 2002. A combined listing of all dissertations and theses , going back to 1934, is available at Georgia Tech's library archive. For the post PhD employment of our graduates see our Alumni Page .
(external link) | |||
Cai, May | Yu, J. | ||
Deslandes, Clement | Houdre, C. | ||
Minahan, Daniel | Margalit, D. and Hom, J. | ||
Omarov, Daniyar | Dieci, L. | ||
Shapiro, Roberta | Margalit, D. and Etnyre, J. | ||
Shu, Kevin | Blekherman, G. | ||
Computational models for bacterial dynamics in community and treatment contexts | Sundius, Sarah | Kuske, R. and Brown, S. (BIOL) | |
Komatsuzaki, Aran | Matzinger, H. | ||
Tang Rajchel, Mengyi | Kang, S. | ||
Acevedo, Jose | Blekherman, G. | ||
Barvinok, Nicholas | Ghomi, M. | ||
Improving and maximal inequalities in discrete harmonic analysis | Giannitsi, Christina | Lacey, M. | |
Gunn, Trevor | Baker, M. | ||
Lee, Chi-Nuo | Croot, E. | ||
Roy, Agniva | Etnyre, J. | ||
Schroeder, Joshua | Yu, X. | ||
Sun, Haoran | Koltchinskii, V. | ||
Sun, Shengding | Blekherman, D. and Dey, S. (ISYE) | ||
Viquez Bolanos, Jorge Aurelio | Houdre, C. | ||
Wigal, Michael | Yu, X. | ||
Wu, Hao | Zhou, H. | ||
Zhang, Tianyi | Baker, M. and Lorscheid, O. (University of Groningen) | ||
Zhou, Hongyi | Hom, J. | ||
A finite difference method on irregular grids with local second order ghost point extension for solving Maxwell's Equations around curved PEC objects | Zou, Haiyu | Liu, Y. | |
Bailey, Victor | Heil, C. | ||
Collins, Sarah | Hom, J. | ||
Harper, David | Damron, M. | ||
Liu, Xiaonan | Yu, X. | ||
Salem, Jad | Gupta, S. | ||
Tate, Reuben | Gupta, S. | ||
Yu, Tao | Le, T. | ||
Duan, Juntao | Matzinger, H. and Popescu, I. | ||
Hozoori, Surena | Etnyre, J. | ||
Ide, Benjamin | Kang, S. | ||
Jung, Jaewoo | Blekherman, G. | ||
Kumar, Bhanu | de la Llave, R. | ||
Liu, Xiao | Zeng, C. | ||
Ma, Shaojun | Zhou, H. | ||
Mousavi, Hamed | Croot, E. | ||
Mukherjee, Anubhav | Etnyre, J. | ||
Qian, Yingjie | Yu, X. | ||
Sabo, Eric | Harrell, E. | ||
Schmidt, Maxie | Yu, J. | ||
Wenk, James | Ghomi, M. | ||
Yoo, Youngho | Yu, X. | ||
Yuan, Xiaofan | Yu, X. | ||
Chen, Xinshi | Song, L. | ||
Harkonen, Marc | Leykin, A. | ||
Stability and Instability of the Kelvin-Stuart Cat's Eyes Flow to the 2D Euler's Equations | Liao, Shasha | Lin, Z. | |
Liu, Shu | Zhou, H. | ||
Olinde, John | Short, M. | ||
Optimal Motion Planning and Computational Optimal Transport | Sun, Haodong | Kang, S. and Zhou, H. | |
Zhu, Xingyu | Belegradek, I. | ||
Perez Bustamante, Adrian | de la Llave, R. | ||
Zhu, Dantong | Thomas, R. and Yu, X. | ||
Attarchi, Hassan | Bunimovich, L. | ||
Chen, Renyi | Tao, M. and Li, G. | ||
Duff, Timothy | Leykin, A. | ||
Guo, He | Warnke, L. | ||
Hill, Cvetelina | Yu, J. | ||
Kirkpatrick, Anna | Mitchell, C. and Tetali, P. | ||
Branched Covers and Braided Embeddings | Kolay, Sudipta | Etnyre, J. | |
Min, Hyun Ki | Etnyre, J. | ||
Yang, Jiaqi | de la Llave, R. | ||
Yiao, Yian | de la Llave, R. | ||
Cheng, Yam-Sung | Heil, C. | ||
He, Yuchen | Kang, S. | ||
Non-parametric Analysis for Time Series Gap Data with Applications in Acute Myocardial Infarction Disease | Li, Hangfan | Houdre, C. | |
Li, Ruilin | Zhou, H. and Zha, H. | ||
Park, Jaemin | Yao, Y. | ||
Spectrum Reconstruction Technique and Improved Naive Bayes Models for Text Classification Problems | Dai, Zhibo | Matzinger, H. | |
Hu, Qianli | Pan, R. | ||
Park, Josiah | Heil, C. and Lacey, M. | ||
Kieffer, Thomas | Loss, M. | ||
Lanier, Justin | Margalit, D. | ||
Lee, Kisun | Leykin, A. | ||
Petti, Samantha | Vempala, S. | ||
Paprocki, Jonathan | Le, T. | ||
Xie, Shijie | Yu, X. | ||
Xing, Xin | Chow, E. and Zhou, H. | ||
Zhang, Yuze | Houdre, C. | ||
Bock, Bounghun | Damron, M. | ||
Celaya, Marcel | Yu, J. | ||
Chen, Jiangning | Matzinger, H. and Lounici, K. | ||
Ghanta, Rohan | Loss, M. | ||
Hoyer, Alexander | Thomas, R. | ||
Mayorga, Sergio | Gangbo, W. and Swiech, A. | ||
McCullough, Andrew | Etnyre, J. | ||
Shu, Longmei | Bunimovich, L. | ||
Zhai, Haoyan | Zhou, H. | ||
Kerchev, George | Houdre, C. | ||
Coloring Graphs with No K5-Subdivision: Disjoint Paths in Graphs | Xie, Qiqin | Yu, X. | |
Liu, Qingqing | Houdre, C. | ||
Scott, Shane | Margalit, D. | ||
Zhou, Fan | Koltchinskii, V. | ||
Chen, Tongzhou | Short, M. | ||
Dever, John | Bellissard, J. and Harrell, E. | ||
Wang, Xin | Liu, Y. | ||
Wang, Yichen | Song, L. and Zhou, H. | ||
Xu, Chen | Houdre, C. | ||
Yuen, Chi Ho | Baker, M. | ||
Bolding, Mark | Bunimovich, L. | ||
Dang, Thanh Ngoc | Thomas, R. | ||
Du, Rundong | Park, H. | ||
Mena Arias, Dario Alberto | Lacey, M. | ||
de Viana, Mikel | de la Llave, R. | ||
Ralli, Peter | Tetali, P. | ||
Hou, Yanxi | Yu, X. | ||
Kunwar, Ishwari | Lacey, M. | ||
Sampson, Donald | McCuan, J. | ||
Spencer, Timothy Scott | Lacey, M. | ||
Tossounian, Hagop | Loss, M. | ||
Walsh, Joseph Donald | Dieci, L. | ||
Wang, Yan | Yu, X. | ||
Zhang, Lei | de la Llave, R. | ||
He, Dawei | Yu, X. | ||
Cohen, Emma | Tetali | ||
Conway, James Irwin | Etnyre | ||
Uniqueness, Existence, and Regularity of solutions of Integro-PDEs in domains of R^n. | Mou, Chenchen | Yi/Swiech | |
Xia, Dong | Koltchinskii | ||
Li, Wuchen | Dieci/Zhou | ||
Difonzo, Fabio Vito | Dieci | ||
Vaidyanathan, Ranjini | Bonetto | ||
Wang, Ruidong | Trotter | ||
Awi, Romeo Olivier | Gangbo | ||
Bush, Albert Robert | Croot | ||
Hu, Jing | Belegradek | ||
Krone, Robert | Leykin | ||
Hoffmeyer, Allen Kyle | Houdre | ||
Hu, Lili | Liu | ||
He, Yunlong | Monteiro, Park | ||
Pryby, Christopher Ian | Croot | ||
Rangel Walteros, Pedro Andres | Koltchinskii | ||
Hurth, Tobias | Bakhtin | ||
Kaloti, Amey Sadanand | Etnyre | ||
Liu, Chun-Hung | Thomas | ||
Luo, Ye | Baker | ||
Vuong, Thao Minh | Garoufalidis | ||
Wang, Xiaolin | Alben/Weiss | ||
Whalen, Peter Michael Zanton | Thomas | ||
Zhang, Weizhe | Pan | ||
Amirkhanyan, Gagik Martuni | Lacey | ||
Backman, Spencer Foster | Baker | ||
Lu, Jun | Zhou | ||
Shin, Hyunshik | Margalit | ||
Winarski, Rebecca Rae | Margalit | ||
Casey, Meredith Perrie | Etnyre | ||
Liu, Jingfang | Zhou | ||
Shokrieh, Farbod | Baker | ||
Yin, Ke | Zhou | ||
Feng, Huijun | Peng | ||
Ni, Kai | Koltchinskii | ||
Scurry, James Wright | Wick | ||
Asadi Shahmirzadi, Arash | Thomas | ||
Ma, Jinyong | Houdre | ||
Postle, Luke Jamison | Thomas | ||
Chenette, Nathan Lee | Thomas | ||
Gong, Ruoting | Houdre | ||
Huynh, Huy Ngoc Quoc | Houdre | ||
Li, Yao | Yi | ||
Minsker, Stanislav | Koltchinskii | ||
Sedjro, Marc Mawulom | Gangbo | ||
Tosun, Bulent | Etnyre | ||
Tran, Anh Tuan | Le | ||
Wang, Ruodu | Peng | ||
Ye, Tianjun | Yu, X. | ||
Gong, Yun | Peng | ||
Streib, Amanda Pascoe | Randall | ||
Streib, Noah Sametz | Trotter | ||
Wu, Jialiang | Voit | ||
Einav, Amit | Loss | ||
Restrepo, Ricardo | Tetali | ||
Chen, Kenneth | Cook | ||
Lu, Nan | Zeng | ||
Ma, Jie | Yu, X. | ||
Sloane, Craig Andrew | Loss | ||
Almada Monter, Sergio Angel | Bakhtin | ||
Reguera Rodriguez, Maria Del Carme | Lacey | ||
Webb, Benjamin Zachary | Bunimovich | ||
Yerger, Carl Roger | Thomas | ||
Howard, David Michael | Trotter | ||
Palmer, Ian Christian | Bellissard | ||
Stefansson, Ulfar Freyr | Lubinsky | ||
Tinaztepe, Ramazan | Heil | ||
Vagharshakyan, Armen Ashot | Lacey | ||
Bishop, Shannon Renee Smith | Heil | ||
Keller, Mitchel Todd | Trotter | ||
Deng, Hao | Zhou | ||
Yildirim Yolcu, Selma | Harrell | ||
Zhao, Kun | Pan | ||
Borenstein, Evan Scot | Croot | ||
Grigo, Alexander | Bunimovich | ||
Kim, Hwa Kil | Gangbo | ||
Yolcu, Turkay | Gangbo | ||
Greenberg, Samuel Gottfried | Randall | ||
Bilinski, Mark | Yu | ||
Li, Yongfeng | Yi | ||
Litherland, Trevis J | Houdre | ||
Xu, Hua | Houdre | ||
Young, Stephen James | Mihail | ||
Yurchenko, Aleksey | Bunimovich | ||
Biro, Csaba | Trotter | ||
Jimenez, David Adrian | Wang | ||
Marcus, Adam Wade | Tetali | ||
Pearson, John Clifford | Bellissard | ||
Pugliese, Alessandro | Dieci | ||
Savinien, Jean Philippe Xavier | Bellissard | ||
Carroll, Christina Conklin | Tetali | ||
Inkmann, Torsten | Thomas | ||
Kampel, Guido | Goldsztein | ||
Kettner, Michael | Basu | ||
Lessard, Jean-Philippe | Mischaikow | ||
Viveros Rogel, Jorge | Yi | ||
Ulusoy, Suleyman | Carlen | ||
Jiang, Wen | Xu | ||
Komendarczyk, Rafal Adam | Ghrist | ||
Hegde, Rajneesh Dattatray | Thomas | ||
Hohenegger, Christel | Mucha | ||
Wollan, Paul Joseph | Thomas | ||
Chen, Jian | Yi | ||
Gameiro, Marcio Fuzeto | Mischaikow | ||
Moeller, Todd Keith | Mischaikow | ||
Norin, Sergey | Thomas | ||
Hernandez-Urena, Luis | Kertz | ||
Sammer, Marcus D | Tetali | ||
Sanchez, Jose Luis Hernandez | Chow | ||
Song, Zixia | Thomas | ||
Figueroa-Lopez, Jose Enrique | Houdré | ||
Kreslavskiy, Dmitry Michael | Bunimovich | ||
Rasmussen, Bryan Michael | Dieci | ||
Curran, Sean Patrick | Yu | ||
Day, Sarah Lynn | Mischaikow | ||
Okoudjou, Kasso Akochaye | Heil | ||
Sheppardson, Laura Jean | Yu | ||
Khlabystova, Milena Alexandrovna | Bunimovich | ||
Wang, Xuelei | Jin | ||
Polygonal Approximation for Flows | Boczko, Erik Miklos | Mischaikow | |
Agueh, Martial Marie-Paul | Gangbo | ||
Del Magno, Gianluigi | Bunimovich | ||
Kelome, Djivede Armel | Swiech | ||
Maroofi, Hamed | Gangbo | ||
Rebaza Vasquez, Jorge Luis | Dieci | ||
Martin, Russell Andrew | Randall | ||
Murali, Shobhana | Houdré | ||
Sitton, David Edward Range | Hill | ||
Burer, Samuel Andrew | Monteiro | ||
Stoyanov, Tzvetan Ivanov | Houdré | ||
Some generalizations of the Knaster-Kuratowski-Mazurkiewicz Theorem | Gonzalez Espinoza, Luis Armando | Cain | |
Jacobs, Denise Anne Kanabroski | Heil | ||
Rivera, Roberto Rafael | Robinson | ||
Thomson, Jan Mcdonald | Thomas | ||
Baker, Anthony Wayne | Mischaikow | ||
Harrelson, Dyana Rae Rice | Houdré | ||
Labate, Demetrio | Heil | ||
McShine, Lisa Maria | Tetali | ||
Vougalter, Vitali Grigor'Evich | Loss | ||
Random Probability Measures with Given Mean and Variance | Bloomer, Lisa A | Hill | |
Heckman, Christopher Carl | Thomas | ||
Kerce, James Clayton | Carlen | ||
Weedermann, Marion | Hale | ||
Hlineny, Petr | Thomas | ||
Klabjan, Diego | Nemhouse/Duke | ||
Walls, Barrett Hamilton | Thomas | ||
Szymczak, Andrzej | Mischaikow | ||
Acosta, Antonio Ramon | Chow | ||
Fowler, Tom George | Thomas | ||
Watson, Greg Malcolm | Mischaikow | ||
Belogay, Eugeni Alexandrov | Wang | ||
O'Connell, Walter Richard | Harrell | ||
Pederson, Steven Michael | Xia | ||
Salazar Gonzalez, Jose Domingo | Hale | ||
Yang, Xue-Feng | Harrell | ||
Kuhn, Zuzana Thomas | Hill | ||
Tan, Bin | Hale | ||
Lara, Pulido Teodoro Del Car | Chow | ||
Carbinatto, Maria Do Carmo | Mischaikow | ||
Keeve, Michael Octavis | Dieci | ||
Kuhn, Wolfgang | Estep | ||
Liu, Weishi | Chow | ||
LaDue, Mark Douglas | Green | ||
Leeds, Kevin N | Shonkwiler | ||
Dai, Wanyang | Dai | ||
Venkatagiri, Shankar C | Bunimovich | ||
Bussian, Eric Richard | Duke | ||
Rehacek, Jan | Bunimovich | ||
Thomas, Diana Maria | Chow | ||
Mendivil, Franklin Arturo | Cain | ||
Rufeger, Waltraud | Ames | ||
Eidenschink, Michael | Mischaikow | ||
Leiva, Hugo | Chow | ||
Meddin, Mona | Shonkwiler | ||
Hardin, Douglas Patten | Barnsley | ||
Banaszuk, Andrzej | Loss | ||
Donovan, George Cassinis | Geronimo | ||
Howard, Timothy Gerard | Herod | ||
Young, Todd Ray | Afraimovich/Chow | ||
Pinto, Joao Teixeira | Hale | ||
Gedeon, Tomas | Mischaikow | ||
Burchard, Almut Dorothea | Loss | ||
Michel, Patricia L | Harrell | ||
Oliva Filho, Sergio Muniz | Hale | ||
Bright, Theresa Ann | Ames | ||
Hines, Gwendolen M | Hale | ||
Sanders, Daniel Preston | Thomas | ||
Kelly, William Benjamin | Meyer | ||
Chen, Mingxiang | Chow | ||
Carvalho, Alexandre Nolasco De | Hale | ||
Shen, Wenxian | Chow | ||
Shieh, Jung-Sheng | Tong | ||
Kwek, Keng-Huat | Chow | ||
Arrieta, Jose M | Hale | ||
Arrigo, Daniel Joseph | Ames | ||
Green, Edward Lee | Harrell | ||
King, James Francis | Geronimo | ||
Kuai, Wenming | Shonkwiler | ||
Van Vleck, Erik Scott | Chow | ||
Postell, Floyd Vince | Ames | ||
James, Glenn Edward | Harrell | ||
Smith, Dale T | Harrell | ||
Jacquin, Arnaud Eric | Barnsley | ||
Jones, Martin Lee | Hill | ||
Abell, Martha Louise | Ames | ||
Lewellen, Gary Boyd | Cain | ||
Patterson, Wanda Mcnair | Andrew | ||
Khadivi, Mohammad Reza | Green | ||
Peters, James Edward | Ames | ||
Brown, Martin Lloyd | Ames | ||
Richards, Pamela Childs | Ames | ||
Womble, David Eugene | Meyer | ||
Massopust, Peter Robert | Barnsley | ||
Herndon, John Alan | Barnsley | ||
Ervin, Vincent John | Ames | ||
Raddatz, William Daniel | Barnsley | ||
Withers, William Douglas | Karlovitz | ||
Bielecki, Daria Jan | Sledd | ||
Mokole, Eric Louis | Sledd | ||
Boisvert, Robert Eugene | Ames | ||
Glidewell, Samuel Ray | Sledd | ||
Hubbard, Elaine Marjorie | Goode | ||
Ingle, Richard Maurice | Stallybrass | ||
Freedman, Michael Aaron | Herod | ||
Jory, Virginia Vickery | Herod | ||
Siegrist, Kyle Travis | Kertz | ||
West, Michael Scott | Sledd | ||
Faulkner, Gary Doyle | Shonkwiler | ||
Kramarz, Luis | Kammerer | ||
Summers, Richard Deane | Stallybrass | ||
Sullivan, Joe Wheeler | Herod | ||
Purdom, Seaton Driskell | Herod | ||
Scherer, Stephen Edwin | Stallybrass | ||
McKibben, William Pullin | Sledd | ||
Christian, William Greer | Sledd | ||
Rollins, Laddie Wayne | Stallard | ||
Lovelady, David Lowell | Herod | ||
Martens, Walter Frederick | Sledd | ||
Reddien, George William | Kammerer | ||
Buckley, James Joseph | Coleman | ||
Lee, Philip Francis | Kurth | ||
Brown, David Lyle | Kasriel | ||
Lucas, Thomas Ramsey | Kammerer | ||
Martin, Robert Harold | Stallard | ||
Wertheimer, Stanley Joseph | Kasriel | ||
Huthnance, Edward Dennis | Robinson | ||
Law, Alan Greenwell | Sledd | ||
Cook, Frederick Lee | Sledd | ||
Fuller, Richard Vernon | Kasriel | ||
Jayne, John William | Sledd | ||
Cain, George Lee | Kasriel | ||
Stiles, Wilbur Janes | Kammerer |
(external link) | |||
Hall, Ariana | Wang, Z. | ||
Ma, Yuanzhe | Damron, M. | ||
Li, Jiaheng | Damron, M. | ||
Hebbe Madhusudhana, Bharath | Blekherman, G. | ||
Elmas, Gokhan | Etnyre | ||
Hurth, Tobias | Bakhtin | ||
Hupp, Phillipp | Harrell | ||
Ford, Allison Elaine | Mucha | ||
Leach, Sandie Patricia | Heil | ||
Goble, Tiffany Danielle | Belinfante | ||
White, Edward C., Jr. | Harrell | ||
Hynd, Ryan Charles | McCuan | ||
Hart, Derrick N. | Lacey | ||
Zickfeld, Florian | Yu | ||
Baamann, Katharina | Mucha | ||
Doto, James William | Carlen |
Mathematical sciences.
Year of Graduation | Student | Supervising Professor | Dissertation Title |
---|---|---|---|
2023 | Nisha Yadav | Anh Tran | THE ALGEBRAIC GEOMETRY OF CHARACTER VARIETIES OF DOUBLE TWIST LINKS |
2023 | Russell Hart | Yifei Lou | Sparsity, Graph Neural Networks and Uncertainty Quantification |
2023 | Bradley Meyer | Anh Tran | LEFT ORDERABILITY OF CYCLIC BRANCHED COVERS OF RATIONAL KNOTS |
2023 | Nishamani Lashika Rajapaksha | Janos Turi | OPTIMAL CONTROL OF HUMAN BALANCE MODELS WITH REFLEX DELAY |
2023 | Hari Prasad Sitaula | Carlos Arreche | Algorithms to Compute Discrete Residues of a Rational Function |
2022 | Sabindra Singh Bal | Viswanath Ramakrishna | INVESTIGATION INTO HIGHER DIMENSIONAL ROTATIONS |
2022 | Josean Albelo-Cortes | Oleg Makarenkov | ANALYSIS OF PLASTIC DEFORMATIONS IN LATTICE SPRING MODELS |
2022 | Jorge Garcia | Tomoki Ohsawa | STABILIZATION OF NONHOLONOMIC EULER–POINCARÉ MECHANICAL SYSTEMS WITH BROKEN SYMMETRY BY CONTROLLED LAGRANGIANS |
2022 | Ali Ahammed Mozumder | Susan Minkoff and John Zweck | MODELING AND SENSITIVITY ANALYSIS FOR TRACE GAS SENSORS |
2022 | Jonathan Popa | Susan Minkoff and Yifei Lou | SEISMIC DATA RECONSTRUCTION WITH LOW-RANK TENSOR OPTIMIZATION |
2022 | Adrian Murza | Zalman Balanov | Periodic Solutions to Reversible Second Order Autonomous DDES in Prescribed Symmetric Nonconvex Domains |
2022 | Augustine Annan | Janos Turi | Forecasting Stock Price Movements and Stock Trading Automation Using Deep Learning and Reinforcement Learning |
2022 | Buddhika Jayawardana | Tomoki Ohsawa | Geometric Integrators for Non-Separable Hamiltonian Systems |
2022 | Nirjal Sapkota | Janos Turi | Stability and bifurcation analysis of a delay differential equation modeling the human respiratory system |
2022 | Priyojit Palit | Nathan Williams | Dual Braid Presentations and Cluster Algebras |
2022 | Subas Acharya | Dmitry Rachinskiy and Alain Bensoussan | Analysis of Real Options and Wealth Management Problems using Non-smooth Variational Inequalities and Asymptotic Methods |
2022 | Vrushaly Shinglot | John Zweck | COMPUTATION AND STABILITY ANALYSIS OF PERIODICALLY STATIONARY PULSES IN A SHORT PULSE LASER |
2022 | Xiaoli Ye | Wieslaw Krawcewicz | Existence and Spatio-Temporal Patterns of Periodic Solutions to Non-Autonomous Second Order Equivariant Delayed Systems |
2021 | Abdoulaye Thiam | Janos Turi | ON INVENTORY CONTROL PROBLEMS WITH LEARNING |
2021 | Aleksandr Milogorodskii | Dmitry Rachinskiy and Michael Ruderman | A Deterministic Model for Non-Monotone Relationship Between Translation of Upstream and Downstream Open Reading Frames |
2021 | Alsadig Ali | Luis Felipe Pereira | MULTISCALE SAMPLING FOR SUBSURFACE CHARACTERIZATION |
2021 | Behshid Kasmaie | Mohammad Akbar | Symmetries of Einstein’s Equations in Vacuum and their Geodesics |
2021 | Cesar Contreras | Tomoki Ohsawa | Controlled Lagrangians and Stabilization of Euler-Poincaré Mechanical Systems with Broken Symmetry |
2021 | Che-Yu Wu | Mieczyslaw Dabkowski | Coefficients of Catalan States of Lattice Crossing |
2021 | Diarisoa Mihaja Rakotomalala | Mieczyslaw Dabkowski | B–TYPE CATALAN STATES OF LATTICE CROSSING |
2021 | Fariba Khoshnasib Zeinabad | Vladimir Dragovic | SOME TOPOLOGICAL ASPECTS OF INTEGRABLE RIGID BODY DYNAMICS |
2021 | Fatih Gelir | Vish Ramakrishna | IDENTIFICATION OF LINEAR CONTROL SYSTEMS VIA GRADIENT DESCENT |
2021 | Izuchukwu Amos Eze | Wieslaw Krawcewicz | Existence and bifurcation of sub-harmonic solutions in reversible non-autonomous differential equations |
2021 | Mehdi Akhavan | Yifei Lou | PHASE RETRIEVAL BY ALTERNATING DIRECTION METHOD OF MULTIPLIERS |
2021 | Mengqi Hu | Yifei Lou | A General Framework of Non-Convex Models for Sparse Recovery with Applications |
2021 | Prosper Akrobotu | Mohammad Akbar | QUANTUM SEARCH ON MOLECULAR GRAPHS AND WORD-REPRESENTABLE LINE GRAPHS |
2021 | Rajendra K. C. Khatri | Yan Cao | CELL NUCLEI SEGMENTATION USING DEEP LEARNING TECHNIQUES |
2021 | Samiha Rouf | Dmitry Rachinskiy and Jana Kopfova | Dynamics of Sir Model with Switching Transmission Rate and Vaccination Rate Characterized by a Relay System or Preisach Operator |
2021 | Siyuan Wang | Yan Cao | Bi-tensor Free Water Model with Positive Definite Diffusion Tensor and Fast Optimization |
2020 | Abdullah Al Mamun | Luis Felipe Pereira | An Assessment of Markov Chain Monte Carlo Methods for Fluid Flow Forecasting in the Subsurface |
2020 | Georgia Stuart | Susan Minkoff and Luis Felipe Pereira | Computationally Efficient methods for Uncertainty Quantification in Seismic Inversion |
2020 | Het Mankad | Luis Felipe Pereira | The Multiscale Perturbation Method for Two-Phase Flows in Porous Media |
2020 | Ivan Gudoshnikov | Oleg Makarenkov | ON THE STABILITY OF MOREAU’S SWEEPING PROCESS WITH APPLICATIONS TO NETWORKS OF ELASTOPLASTIC SPRINGS |
2020 | Joseph Burnett | Wieslaw Krawcewicz and Zalman Balanov | Global Bifurcation of Periodic Solutions in Symmetric Reversible Second Order Systems with Delays |
2020 | Md Abu Helal | Viswanath Ramakrishna | MATHEMATICAL METHODS FOR ADVANCED PROBLEMS OF INVENTORY CONTROL |
2020 | Md Arafat Khan | Anh Tran | Left Orderability of Dehn Surgery on Odd Classical Pretzel Knots |
2020 | Md Mujibur Chowdhurv | Yifei Lou | Fractional-Order Total Variation Based Image Denoising, Deconvolution, and CT Reconstruction Under Poisson Statistics |
2020 | Samreen Khan | Viswanath Ramakrishna | Polar and Givens Decomposition and Inversion of the Indefinite Double Covering Map |
2020 | Samson Folarin | Viswanath Ramakrishna | Reservoir Characterization of Non Gaussian Field Using Combined Ensemble Based Method |
2020 | Sonam Lama | John Zweck and Matthew Goeckner | The Stochastic Weighted Particle Method for the Computation of the low Probability Tail of the Velocity Distribution in Spatially Homogeneous Plasmas |
2019 | Anani Adabrah Komla | Vladimir Dragovic | QUADRICS IN PSEUDO-EUCLIDEAN SPACES, INTEGRABLE BILLIARDS AND EXTREMAL POLYNOMIALS |
2019 | Charles Chika | M. Ali Hooshyar | A NON-ITERATIVE CONSTRUCTION OF A CLASS OF 2-D WAVE SPEED FROM FORWARD SCATTERING DAT |
2019 | Irina Berezovik | Wieslaw Krawcewicz | Classification of Nonlinear Vibrations in Symmertric Molecules: Equivariant Degree Method |
2019 | Pavel Kravetc | Dmitry Rachinskiy | APPLICATIONS OF TOPOLOGICAL AND PERTURBATION METHODS TO ANALYSIS OF PERIODIC SOLUTIONS IN DELAY-DIFFERENTIAL EQUATIONS: CLASSIFICATION OF SYMMETRIES, ASYMPTOTIC APPROXIMATION AND STABILIZATION |
2019 | Roger F. Ranomenjanahary | Vladimir Dragovic | GEOMETRIC AND COMBINATORIAL PROPERTIES OF NETS IN PLANE AND HIGHER-DIMENSIONS |
2019 | Shi Yu | Wieslaw Krawcewicz | EXISTENCE AND BIFURCATION OF PERIODIC SOLUTIONS IN SECOND ORDER NONLINEAR SYSTEM: BROUWER EQUIVARIANT DEGREE METHOD |
2018 | Artur Safin | John Zweck and Susan Minkoff | Modeling Trace Gas Sensors with the Coupled Pressure-Temperature Equations |
2018 | Edward Hooton | Dmitry Rachinskiy and Zalman Balanov | Existence and Stabilization of Periodic Solutions in Equivariant Systems |
2018 | Filip Jevtic | Vladimir Dragovic | Combinatorial Structure of Finite Metric Spaces |
2018 | Hao-Pin Wu | Zalman Balanov and Wieslaw Krawcewicz | Applications of Degree Theory to Dynamical Systems with Symmetry (with special focus on Computational Aspects and Algebraic Challenges) |
2018 | Jordan Kaderli | Susan Minkoff | An Analytic Solution to a coupled system of equations for Modeling Photoacoustic Trace Gas Sensors and a full Waveform Inversion Approach to Microseismic Source Information |
2018 | Lakmi N. W. Achchige | Oleg Makarenkov | Stability, Bifurcation, and Continuation Theory for Perturbed Sweeping Processes |
2017 | Eyram Kwame | Dmitry Rachinskiy | Mathematical Modeling for Applications in Economics |
2017 | Isnardo Arenas-Navarro | Susan Minkoff and Stefano Leonardi | Numerical Simulations for Turbulent Drag Reduction Using Liquid Infused Surfaces |
2017 | Pedro Perez-Nagera | Janos Turi | Numerical Solutions for a Class of Singular Neutral Functional Differential Equation |
2016 | Emily Herzig | Viswanath Ramakrishna | Spin Groups and Exponentiation |
2016 | Sonny Skaaning | Janos Turi and Alain Bensoussan | Inventory Control with Pricing Optimization in Continuous Time |
2016 | Yanping Chen | John Zweck and Matthew Goeckner | Computational Modeling of Collision Processes in Low Temperature Plasmas |
2015 | Farzan Jafeh | Mieczyslaw Dabkowski and Zalman Balanov | Congruence Principle for Brouwer Degree of Equivariant Maps between Solvable Group Representation Spheres |
2015 | Yanli Lv | Wieslaw Krawcewicz | New Equivariant Methods and Applications to Symmetric Differential Equations |
2015 | Zachary Elewitz | Tobias Hagge | Detection of the Reidemeister 2-Move Via Generalized Polyak Invariants |
2014 | Changsong Li | Mieczyslaw Dabkowski | Multiplicative Structure on KBSM of I-Bundle Over a Disk with Three Punctures |
2014 | Zhichao Li | Wieslaw Krawcewicz | Symmetric Systems of Implicit Functional Differential Equations: Existence of Solutions and Bifurcation Results |
2013 | Minh P. Nguyen | Yan Cao | Shape Analysis Using Geometric Features and Diffeomorphic Deformation |
2013 | My Linh Nguyen | Zalman Balanov | Symmetric Boundary Value Problems for Vector Nonlinear Pendulum Equation: Equivariant Degree Approach |
2012 | Ajaya Paudel | M. Ali Hooshyar | An Inverse Scattering Problem for the Two Dimensional Helmholtz Equation |
2011 | Billye Cheek | Mieczyslaw Dabkowski | Kauffman Bracket Skein Module for the Disk Sum of A x S1 and A x I |
2011 | Brady McCary | Yan Cao | User-Interactive Level Set Image Segmentation |
2010 | Jigarkumar Patel | Janos Turi | Elastic Structures with Defects |
2010 | Keerthi P. K. Chandrasekaran | Janos Turi | Optimal Control of Piecewise Smooth Systems |
2010 | Saroj Pradhan | Janos Turi | The Role of Peripheral and Central Chemoreceptors in Stability of the Human Respiratory System |
2009 | Noureen Khan | Mieczyslaw Dabkowski | New Variants of Links in S3 Preserved by 4-Moves |
2008 | Yasmin Ansari | Viswanath Ramakrishna | Matrix Theory Motivated by Quantum Mechanics and Engineering |
2007 | Ramanjit Sahi | Mieczyslaw Dabkowski | Tangle Replacement Moves on Links |
2006 | Hong Zhou | Viswanath Ramakrishna | Parameterizations of Unitary and Positive Matrices in Quantum Information Control |
2006 | Nermine El-Sissi | Viswanath Ramakrishna | Positive Definite Kernels and Lattice Paths |
2005 | Fred Costa | Viswanath Ramakrishna | Structured Matrix Calculations via Quaternions |
2005 | Lena Lasater | M. Ali Hooshyar | Inverse Problems of Electromagnetic Obstacle Scattering and the Method of Lines |
2005 | Taras Odushkin | Janos Turi | Mathematical Models of Atomic Scale Deformations and Spatial Nonuniformities in Solid Bodies |
2003 | David Seida | Janos Turi | Estimation of Attitude Parameters from Variation in Image Overlap |
2002 | Kathryn Flores | Viswanath Ramakrishna | Classical and Quantum Controls from Decomposition of Unitary Matrices |
Julius baldauf.
Date: Thursday, March 28, 2024 | 2:10pm | Room: 2-449 | Zoom Link
Committee: Bill Minicozzi (Thesis Advisor and Examination Committee Chair), Tristan Collins, Tristan Ozuch
The Ricci Flow on Spin Manifolds
This thesis studies the Ricci flow on manifolds admitting harmonic spinors. It is shown that Perelman's Ricci flow entropy can be expressed in terms of the energy of harmonic spinors in all dimensions, and in four dimensions, in terms of the energy of Seiberg-Witten monopoles. Consequently, Ricci flow is the gradient flow of these energies. The proof relies on a weighted version of the monopole equations, introduced here. Further, a sharp parabolic Hitchin-Thorpe inequality for simply-connected, spin 4-manifolds is proven. From this, it follows that the normalized Ricci flow on any exotic K3 surface must become singular.
Date: Tuesday, June 25, 2024 | 3:00pm | Room: 2-136 | Zoom Link
Committee: Tomasz Mrowka (Advisor and Chair), Daniel Alvarez-Gavela and John Baldwin (Boston College)
Surgery Exact Triangles in Instanton Theory
The introduction of instanton Floer theory and Donaldson polynomial invariants in the 1980s revolutionised the study of low dimensional topology. Since then, many Floer theories have been introduced with different structural properties and qualitative features. One of these Floer theories, Heegaard Floer theory, is popular due to its computational ease and rich algebraic structure. One of the computational tools absent in other Floer theories is the integer surgery formula that computes Heegaard Floer homology of 3-manifolds obtained by surgery along knot(s) in them.
This thesis establishes a new surgery formula in instanton Floer theory. The algebraic language to express this formula is that of the derived category of chain complexes. The first part of the thesis describes this surgery formula whose statement and proof are inspired by the Atiyah-Floer conjectures. The second part then contrasts with the Heegaard Floer analogue by showing that instanton and Heegaard Floer theory cannot agree over integers.
Date: Tuesday, April 30, 2024 | 3:00pm | Room: 4-149 | Zoom Link
Committee: Alexander Rakhlin (advisor), Yury Polyanskiy, Martin Wainwright, Ankur Moitra (chair)
Smoothed Online Learning: Theory and Applications
Many of the algorithms and theoretical results surrounding modern machine learning are predicated on the assumption that data are independent and identically distributed. Motivated by the numerous applications that do not satisfy this assumption, many researchers have been interested in relaxations of this condition, with online learning being the weakest such assumption. In this setting, the learner observes data points one at a time and makes predictions, before incorporating the data into a training set with the goal of predicting new data points as well as possible. Due to the lack of assumptions on the data, this setting is both computationally and statistically challenging. In this thesis, we investigate the statistical rates and efficient algorithms achievable when the data are constrained in a natural way motivated by the smoothed analysis of algorithms. The first part covers the statistical rates achievable by an arbitrary algorithm without regard to efficiency, covering both the fully adversarial setting and the constrained setting in which improved rates are possible. The second part of the thesis focuses on efficient algorithms for this constrained setting, as well as special cases where bounds can be improved under additional structure. Finally, in the third part we investigate applications of these techniques to sequential decicions making, robotics, and differential privacy. We introduce a number of novel techniques, including a Gaussian anti-concentration inequality and a new norm comparison for dependent data.
Date: Monday, July 1, 2024 | 10:30am | Room: 2-361 | Zoom Link
Committee: Prof. Gigliola Staffilani (advisor and committee chair), Prof. Semyon Dyatlov and Prof. Larry Guth
Self-similar singularity formation and wellposedness theory for compressible fluids and dispersive PDE
Date: Tuesday, April 23, 2024 | 11:00am | Room: 4-370
Committee: Wei Zhang, Zhiwei Yun and Spencer Leslie (Boston College)
First explicit reciprocity law for unitary Friedberg—Jacquet periods
In the early 2000's, Bertolini and Darmon introduced a new technique to bound Selmer groups of elliptic curves via level raising congruences. This was the first example of what is now termed a "bipartite Euler system", and over the last decade we have seen many breakthroughs on constructing such systems for other Galois representations, including settings such as twisted and cubic triple product, symmetric cube, and Rankin—Selberg, with applications to the Bloch—Kato conjecture and to Iwasawa theory.
This thesis studies the case of Galois representations attached to automorphic representations on a totally definite unitary group U(2r) over a CM field which are distinguished by the subgroup U(r) x U(r). We prove a new "first explicit reciprocity law" in this setting, which has applications to the rank 0 case of the corresponding Bloch—Kato conjecture.
Date: Wednesday, April 24, 2024 | 3:00pm | Room: 2-142
Committee: Wei Zhang, Julee Kim, Zhiwei Yun
Local newforms and spherical characters for unitary groups
We first prove a smooth transfer statement analogous to Jacquet–Rallis’s fundamental lemma and use it to compute the special value of a local spherical character that appears in the Ichino–Ikeda conjecture at a test vector. Then we provide a uniform definition of newforms for representations of both even and odd dimensional unitary groups over p-adic fields. This definition is compatible with the one given by Atobe, Oi, and Yasuda in the odd dimensional case. Using the nonvanishing of the local spherical character at the test vector, we prove the existence of the representation containing newforms in every tempered Vogan L-packet. We also show the uniqueness of such representations in Vogan L-packets and give an explicit description of them using local Langlands correspondence.
Date: Friday, April 26, 2024 | 9:30am | Room: 2-361 | Zoom Link
Committee: Philippe Rigollet (advisor), Yury Polyanskiy, Martin Wainwright
Likelihood-Free Hypothesis Testing and Applications of the Energy Distance
The first part of this thesis studies the problem of likelihood-free hypothesis testing: given three samples X,Y and Z with sample sizes n,n and m respectively, one must decide whether the distribution of Z is closer to that of X or that of Y. We fully characterize the problem's sample complexity for multiple distribution classes and with high probability. We uncover connections to two-sample, goodness of fit and robust testing, and show the existence of a trade-off of the form mn ~ k/ε^4, where k is an appropriate notion of complexity and ε is the total variation separation between the distributions of X and Y. We demonstrate that the family of "classifier accuracy" tests are not only popular in practice but also provably near-optimal, recovering and simplifying a multitude of classical and recent results. We generalize our problem to allow Z to come from a mixture of the distributions of X and Y, and propose a kernel-based test for its solution. Finally, we verify the existence of a trade-off between m and n on experimental data from particle physics.
In the second part we study applications of the energy distance to minimax statistics. We propose a density estimation routine based on minimizing the generalized energy distance, targeting smooth densities and Gaussian mixtures. We interpret our results in terms of half-plane separability over these classes, and derive analogous results for discrete distributions. As a consequence we deduce that any two discrete distributions are well-separated by a half-plane, provided their support is embedded as a packing of a high-dimensional unit ball. We also scrutinize two recent applications of the energy distance in the two-sample testing literature.
Date: Thursday, April 25, 2024 | 10:00am | Room: 32-G882 | Zoom Link
Committee: Alan Edelman, Steven Johnson, John Urschel
Symbolic-numeric programming in scientific computing
Scientific programming languages should pursue two goals: closeness to mathematical notation, and the ability to express efficient numerical algorithms. To meet these goals simultaneously, languages use imperative surface syntaxes that mimick mathematical notation. However, mimicking does not make them the same—mathematics is declarative, pliable, and caters to exploratory human nature; but algorithms are imperative and must cater to machines. Hence, there is a fundamental limit to this approach and we leave the expressive power of the symbolic representation on the table.
In this thesis, we ask the question: How can symbolic and numerical modes of computing co-exist, one informing the other? As an answer, we develop a user-extensible system that lifts numerical code into symbolic expressions and can turn symbolic expressions back into high-quality numerical code at staged compilation time, essentially providing the scientific user a way to generate programs and to treat programs as the symbolic artifacts they are. We identified siloing of symbolic software into 3 categories (one can call them “symbolic-only”, “secretly symbolic”, “secretly numerical”) which currently each reproduce similar forms of symbolic capabilities, but cannot share code between each other. Our work demonstrates that this siloing is not essential and an ecosystem of symbolic-numeric libraries can thrive in symbiosis.
Our system is adaptable to any domain: users can define 1) Symbolic variables of any type 2) the set of primitive (symbolically indivisible) functions in the domain, 3) the propa- gation of partial information, and 4) pattern-based rewrites and simplification rules. There is a tendency in scientific computing to create a “compiler for every problem” starting from scratch every time. Every such effort erects its own towers of symbolic and numerical ca- pabilites. A system like ours eliminates this redundancy and lets every scientific user be a “compiler designer” without any prior knowledge of compiler development.
Date: Thursday, April 18, 2024 | 10:30am | Room: 2-449 | Zoom Link
Committee: Jörn Dunkel (chair), John Bush, Alexander Mietke
Robust spectral representations and model inference for biological dynamics
Current developments in automated experimental imaging allow for high-resolution tracking across various scales, from whole animal behavior to tissue scale single-cell trajectories during embryogenesis to spatiotemporal gene expression dynamics or neural dynamics. Transforming these high-dimensional data into effective low-dimensional models is an essential theoretical challenge that enables the characterization, comparison, and prediction of the dynamics within and across biological systems. Spectral mode representations have been used successfully across physics, from quantum mechanics to fluid dynamics, to compress and model dynamical data. However, their use in analyzing biological systems has yet to become prevalent. Here, we present a set of noise-robust, geometry-aware mathematical tools that enable spectral representations to extract quantitative measurements directly from experimental data. We demonstrate the practical utility of these methods by applying them to the extraction defect statistics in signaling fields on membranes of starfish, the inference of partial differential equations directly from videos of active particle dynamics, and the categorization of emergent patterns in spatiotemporal gene expression during bacterial swarming.
An additional challenge occurs for complex biophysical processes where the underlying dynamics are yet to be entirely determined. Therefore, we would like to use the experimental data to infer effective dynamical models directly that can elucidate the system's underlying biological and physical mechanisms. Building on spectral mode representations, we construct a generic computational framework that can incorporate prior knowledge about biological and physical constraints for inferring the dynamics of living systems through the evolution of their mode representations. We apply this framework first to single-cell imaging data during zebrafish embryogenesis, demonstrating how our framework compactly characterizes developmental symmetry breaking and reveals similarities between pan-embryo cell migration and Brownian particles on curved surfaces. Next, we apply the framework to the undulatory locomotion of worms, centipedes, robots, and snakes to distinguish between locomotion behaviors. Finally, we present an extension of the framework to the case of nonlinear dynamics when all relevant degrees of freedom are only partially observed, with applications to neuronal and chemical dynamics.
Date: Tuesday, April 23, 2024 | 1:00pm | Room: 1-273 | Zoom Link
Committee: Pavel Etingof (advisor), Roman Bezrukavnikov, Victor Kac
On Lie Theory in the Verlinde Category
A symmetric tensor category (STC) can be thought of as a “home” to do commutative algebra, algebraic geometry, and Lie theory. They are defined by axiomatizing the basic properties of a representation category of a group (or affine supergroup scheme). Are these the only examples of STCs? In characteristic zero, a famous theorem of Deligne states that, assuming a natural growth condition, representation categories of affine supergroup schemes are the only examples. However, the situation is totally different in positive characteristic, and the Verlinde category Verp is the most fundamental counterexample and appears to play a key role in generalizing the theorem of Deligne to positive characteristic. Moreover, Verp contains the category of supervector spaces. The upshot is that the study of Verp provides new algebraic structures and phenomena beyond that afforded by superalgebra and supergeometry but must also generalize what is already known.
In this thesis defense, we will first survey the theory of symmetric tensor categories. Then, we will discuss new algebraic structures that arise from the Verlinde category, including new constructions of exceptional Lie superalgebras and a generalization of Jordan algebras unique to characteristic 5. Finally, we will turn to progress made on generalizing useful algebraic techniques and machinery from the super setting to the Verp setting, like the Steinberg tensor product theorem and notions of polynomial functors.
Date: Tuesday, April 16, 2024 | 2:30pm | Room: 2-131
Committee: Pavel Etingof, Roman Bezrukavnikov and Ivan Loseu (Yale)
Positive traces and analytic Langlands correspondence
I will describe my results with co-authors in two directions.
The first direction is the problem of classification of positive traces on quantized Coulomb branches. In the most general setting, this problem generalizes the classical problem of describing irreducible unitary representations of real reductive Lie groups. We consider the case of Kleinian singularities of type $A$ and provide a complete classification of positive traces.
The second direction is analytic Langlands correspondence, which is the following. Let $X$ be a smooth irreducible projective curve over $\mathbb{C}$, $G$ be a complex reductive group. On one side of this conjectural correspondence there are $G^{\vee}$-opers on $X$ satisfying a certain topological condition ({\it real} opers), where $G^{\vee}$ is Langlands dual group. On the other side there is joint spectrum of certain operators on $L^2(Bun_G)$, called Hecke operators, where $Bun_G$ is the variety of stable parabolic $G$-bundles on $X$ and $L^2(Bun_G)$ is a Hilbert space of square-integrable half-densities. We prove most of the main conjectures of analytic Langlands correspondence in the case when $G=\operatorname{PGL}_2(\mathbb{C})$ and $X$ either a genus one curve with points or $X$ is $\mathbb{P}^1$ with higher structures at points.
Date: Monday, April 29, 2024 | 9:30am | Room: 2-143
Committee: Roman Bezrukaunikov (advisor), Zhiwei Yun, and Ivan Loseu (Yale)
Geometry and representation theory of symplectic singularities in the context of symplectic duality
This thesis studies the geometry and representation theory of various symplectic resolutions of singularities from different perspectives. Specifically, we establish a general approach to attack the Hikita-Nakajima conjecture and illustrate this approach in the example of ADHM spaces. We also study minimally supported representations of the quantizations of ADHM spaces and provide explicit formulas for their characters. Lastly, we describe the monodromy of eigenvalues of quantum multiplication operators for type A Nakajima quiver varieties by examining Bethe subalgebras in Yangians and linking their spectrum with Kirillov-Reshetikhin crystals.
Date: Monday, April 1, 2024 | 3:00pm | Room: 2-361 | Zoom Link
Committee: Prof. Paul Seidel (thesis advisor), Prof. Pavel Etingof, Prof. Denis Auroux (External, Harvard)
Equivariant quantum connections in positive characteristic
Date: Tuesday, April 23, 2024 | 1:30pm | Room: 13-1143
Committee: Davesh Maulik, Michael Hopkins, Haynes Miller, and Jeremy Hahn
The algebraic K-theory of the chromatic filtration and the telescope conjecture
Chromatic homotopy theory gives a conceptual framework with which to understand the stable homotopy theory, by decomposing the stable homotopy category into monochromatic pieces. There are two variants of these monochromatic pieces, the K(n) and T(n)-local categories, the former of which is often quite understandable in terms of formal groups of height n, and the latter of which detects the so-called v_n-periodic part of the stable homotopy groups of spheres. I will explain how algebraic K-theory has refined our understanding of these monochromatic pieces. On one hand, algebraic K-theory is an important structural invariant of these categories that 'stably' classifies objects and their automorphisms, and I will explain some tools we have to computationally access the K-theory of these categories. On the other hand, the algebraic K-theory of such categories are interesting as spectra: they detect a lot of information about the stable homotopy groups of spheres and have helped us understand the difference between the T(n) and K(n)-local categories.
Date: Tuesday, July 2, 2024 | 11:00am | Room: 2-142
Committee: John Bush, Matthew Durey, and Rodolfo Ruben Rosales
Orbital stability in a classical pilot-wave system
The hydrodynamic bouncing droplet system, consisting of millimetric droplets bouncing on a vibrating fluid bath, displays many quantum mechanical phenomena on a macroscopic scale. These phenomena include tunnelling, diffraction and wave-like statistics. This thesis focuses on the features responsible for the quantisation of orbital radii, and rationalises this quantisation in terms of the stability of circular orbits arising in the presence of a rotating frame and a central force, and are most pronounced when the waves generated by each bounce decay slowly. The faster the waves decay, the less past impacts affect the droplet’s future dynamics, corresponding to lower path memory. We conduct an analytical investigation into the stability of circular orbits using a generalized theoretical framework that allows for an exploration of classical pilot-wave dynamics both inside and outside the experimentally accessible parameter regime. The exploration of parameter regimes beyond those accessible with the hydrodynamic system reveals much richer orbital dynamics. Our novel mathematical approach allows for evaluation of the integrals appearing in the stability problem in terms of Bessel functions of complex order, and thus facilitates asymptotic expansions of the stability problem in various limits. Within the experimental parameter regime, we demonstrate that in a rotating frame, circular orbits destabilise only via resonant instabilities, for which the growing perturbations oscillate at a frequency that is an integer multiple of the orbital frequency. Conversely, in a central force, non-resonant instabilities arise, for reasons discussed herein. Outside the experimental parameter regime, we show how the non-resonant instability leads to counter-intuitive scenarios; for example, where circular orbits are stabilised by increasing memory. In the limit of vanishing particle inertia, infinite path memory and a linear spring force, we demonstrate the intriguing possibility of infinitely many sharply quantised orbital states, where the allowed orbital radii exist in vanishingly thin intervals, and are stabilised by the combined influence of the time-averaged wave field and spring force. We demonstrate that these sharply quantised orbital states are only stable for higher memory. We then consider the effect of weak external forces on spin states, circular orbits arising in the absence of external forces, and show that the destabilisation of spin states depends in a complex manner on the type of external force applied. Finally, we show that the instability of large circular orbits is related to the in-line speed oscillations of free walking droplets in a manner that is independent of the external force.
Date: Friday, April 26, 2024 | 1:30pm | Room: 2-449 | Zoom Link
Committee: Roman Bezrukavnikov (advisor), Zhiwei Yun, Ivan Loseu
Kazhdan-Laumon categories and representations
In 1988, D. Kazhdan and G. Laumon constructed the \emph{Kazhdan-Laumon category}, an abelian category $\mathcal{A}$ associated to a reductive group $G$ over a finite field, with the aim of using it to construct discrete series representations of the finite Chevalley group $G(\mathbb{F}_q)$. The well-definedness of their construction depended on their conjecture that this category has finite cohomological dimension. This was disproven by R. Bezrukavnikov and A. Polishchuk in 2001, who found a counterexample for $G = SL_3$.
Since the early 2000s, there has been little activity in the study of Kazhdan-Laumon categories, despite them being beautiful objects with many interesting properties related to the representation theory of $G$ and the geometry of the basic affine space $G/U$. In the first part of this thesis, we conduct an in-depth study of Kazhdan-Laumon categories from a modern perspective. We first define and study an analogue of the Bernstein-Gelfand-Gelfand Category $\mathcal{O}$ for Kazhdan-Laumon categories and study its combinatorics, establishing connections to Braverman-Kazhdan's Schwartz space on the basic affine space and the semi-infinite flag variety. We then study the braid group action on $D^b(G/U)$ (the main ingredient in Kazhdan and Laumon's construction) and show that it categorifies the \emph{algebra of braids and ties}, an algebra previously studied in knot theory; we then use this to provide conceptual and geometric proofs of new results concerning this algebra.
After Bezrukavnikov and Polishchuk's counterexample to Kazhdan and Laumon's original conjecture, Polishchuk made an alternative conjecture: though this counterexample shows that the Grothendieck group $K_0(\mathcal{A})$ is not spanned by objects of finite projective dimension, he noted that a graded version of $K_0(\mathcal{A})$ can be thought of as a module over Laurent polynomials and conjectured that a certain localization of this module is generated by objects of finite projective dimension. He suggested that this conjecture could lead toward a proof that Kazhdan and Laumon's construction is well-defined, and he proved this conjecture in Types $A_1, A_2, A_3$, and $B_2$. In the final chapter of this thesis, we prove Polishchuk's conjecture for all types, and prove that Kazhdan and Laumon's construction is indeed well-defined, giving a new geometric construction of discrete series representations of $G(\mathbb{F}_q)$.
Date: Monday, April 29, 2024 | 2:30pm | Room: 2-361 | Zoom Link
Committee: Alexei Borodin (Advisor, chair), Scott Sheffield, Lauren Williams (Harvard)
Title: Stochastic Dynamics on Integrable Lattice Models
The purpose of this thesis is to present some new results related to the six-vertex and dimer model. One theme is the construction and analysis of Markov processes which are naturally associated to these lattice models. Certain integrability properties of the six-vertex and dimer model, often related to the Yang--Baxter equation, allow for the construction of associated Markov chains. In some cases, these are measure preserving Markov chains on configurations of the lattice model. In other cases, they arise via transfer matrices, after choosing a distinguished time coordinate, as a continuous time degeneration of the "time evolution" of the lattice model itself. It is often the case that the integrability of the underlying lattice model provides powerful tools to study the associated Markov chains or their marginals, which are sometimes Markov chains themselves.
In particular together with coauthors, we construct and analyze Markov chains on six-vertex configurations and on dimer model configurations, both of which are models for surface growth in the (2+1)-dimensional "Anisotropic KPZ" (or "AKPZ") universality class; we construct a Markov chain generalizing "domino shuffling" which samples exactly from a recently introduced probability measure on tuples of interacting dimer configurations; using a version of the usual domino shuffling algorithm, we construct and analyze deterministic "t-embeddings" of certain dimer graphs, which discretize minimal surfaces carrying the conformal structure of the limiting Gaussian free field; we construct stationary measures for several colored interacting particle systems using the Yang—Baxter equation.
Date: Wednesday, April 24, 2024 | 1:15pm | Room: 2-449 | Zoom Link
Committee: Larry Guth (advisor), David Jerison, Gigliola Staffilani
Sparse Fourier restriction for the cone
If the Fourier transform of F(x) is supported near a segment of the light-cone in R^3, what is the shape of the level sets U(N) = {x in R^3 : |F(x)| > N} for large values of N? In 2000, Thomas Wolff had a creative idea to study a related question based on the method of point-circle duality, and used it in a pivotal way to prove the first sharp L^p-decoupling estimates for the cone in R^3 for large values of p.
I will discuss new weighted L^2 estimates of F(x) which give us insight into the shape of level sets. I will explain how we use some of the same key ideas introduced by Wolff, together with a few new ones in the same spirit. By Wolff's method, our main theorem will partly be an application of a recent circular maximal function estimate due to Pramanik—Yang—Zahl in 2022 from their study of Kaufman-type restricted projection problems.
Date: Wednesday, April 3, 2024 | 3:30pm | Room: 2-449
Committee: Prof. Yufei Zhao (advisor and chair), Prof. Dor Minzer, and Prof. Philippe Rigollet
Random and exact structures in combinatorics
We aim to show various developments related to notions of randomness and structure in combinatorics and probability. One central notion, that of the pseudorandomness-structure dichotomy, has played a key role in additive combinatorics and extremal graph theory. In a broader view, randomness (and the pseudorandomness notions which resemble it along various axes) can be viewed as a type of structure in and of itself which has certain typical and global properties that may be exploited to exhibit or constrain combinatorial and probabilistic behavior.
These broader ideas often come in concert to allow the construction or extraction of exact behavior. We look at three particular directions: the singularity of discrete random matrices, thresholds for Steiner triple systems, and improved bounds for Szemerédi's theorem. These concern central questions of the areas of random matrices, combinatorial designs, and additive combinatorics.
Date: Wednesday, April 17, 2024 | 2:00pm | Room: 2-449
Committee: Yufei Zhao, Dor Minzer, and Philippe Rigollet
Probabilistic and Analytic Methods in Combinatorics
The defense will center on fast algorithms for discrepancy theory. Discrepancy theory is broadly concerned with the following problem; given a set of objects, we aim to partition them into pieces which are “roughly equal”. We will focus specifically on vector balancing: given a set of vectors, one seeks to divide them into two parts with approximately equal sum.
Important results in this area, including Spencer’s six standard deviations suffice and Banaszczyk's results towards the Komlós conjecture, were originally purely existential. However, since work of Bansal from 2010, it has become clear that such existential results can often be made algorithmic. We will explain a pair of such results. The first concerns bounds for online vector balancing obtained via a certain Gaussian fixed point random walk. The second gives an algorithmic form of Spencer's theorem that runs in near input sparsity time.
Date: Thursday, April 25, 2024 | 2:30pm | Room: 4-149 | Zoom Link
Committee: Philippe Rigollet, Jörn Dunkel, Sasha Rakhlin
Inference from Limited Observations in Statistical, Dynamical, and Functional Problems
Observational data in physics and the life sciences comes in many varieties. Broadly, we can divide datasets into cross-sectional data which record a set of observations at a given time, dynamical data which follow how observations change in time, and functional data which observe data points over a space (and possibly time) domain. In each setting, prior knowledge of statistical, dynamical systems, and physical theory allow us to constrain the inferences and predictions we make from observational data. This domain knowledge becomes of paramount importance when the data we observe is limited: due to missing labels, small sample sizes, unobserved variables, and noise corruption.
This thesis explores several problems in physics and the life sciences, where the interplay of domain knowledge with statistical theory and machine learning allows us to make inferences from such limited data. We begin in Part I by studying the problem of feature matching or dataset alignment which arises frequently when combining untargeted (unlabeled) biological datasets with low sample sizes. Leveraging the fast numerical methods of optimal transport, we develop an algorithm that gives a state-of-the-art solution to this alignment problem with optimal statistical guarantees. In Part II we study the problem of interpolating the dynamics of points clouds (e.g., cells, particles) given only a few sparse snapshot recordings. We show how tools from spline interpolation coupled with optimal transport give efficient algorithms returning smooth dynamically plausible interpolations. Part III of our thesis studies how dynamical equations of motion can be learned from time series recordings of dynamical systems when only partial observations of these systems are captured in time. Here we develop fast routines for gradient optimization and novel tools for model comparison to learn such physically interpretable models from incomplete time series data. Finally, in Part IV we address the problem of surrogate modeling, translating expensive solvers of partial differential equations for physics simulations into fast and easily-trainable machine learning algorithms. For linear PDEs, our prior knowledge of PDE theory and the statistical theory of kernel methods allows us to learn the Green's functions of various linear PDEs, offering more efficient ways to simulate physical systems.
Date: Wednesday, April 3, 2024 | 2:00pm | Room: 2-255
Committee: Scott Sheffield (advisor), Alexei Borodin, Nike Sun
Conformal welding of random surfaces from Liouville theory
Liouville quantum gravity (LQG) is a natural model describing random surfaces, which arises as the scaling limit for random planar maps. Liouville conformal field theory (LCFT) is the underlying 2D CFT that governs LQG. Schramm-Loewner evolution (SLE) is a random planar curve, which describes the scaling limits of interfaces in many statistical physics models. As discovered by Sheffield (2010), one of the deepest results in random geometry is that SLE curves arises as the interfaces under conformal welding of LQG surfaces.
In this thesis, we present some new results on conformal welding of LQG surfaces as well as their applications towards the theory of SLE. We first define a three-parameter family of random surfaces in LQG which can be viewed as the quantum version of triangles. Then we prove the conformal welding result of a quantum triangle and a two-pointed quantum disk, and deduce integrability results for chordal SLE with three force points.
The second main result is regarding the conformal welding of a multiple number of LQG surfaces, where under several scenarios, we prove that the output surfaces can be described in terms of LCFT, and the random moduli of the surface is encoded in terms of the partition functions for the SLE curves.
The third part is about the conformal welding of the quantum disks with forested boundary, where we prove that this conformal welding gives a two-pointed quantum disk with an independent SLE$_\kappa$ for $\kappa\in(4,8)$. We further extend to the conformal welding of a multiple number of forested quantum disks, where as an application, for $\kappa\in(4,8)$, we prove the existence of the multiple SLE partition functions, which are smooth functions satisfying a system of PDEs and conformal covariance. This was open for $\kappa \in (6,8)$ and $N\ge 3$ prior to our work.
The conformal loop ensemble (CLE) is a random collection of planar loops which locally look like SLE. For $\kappa \in (4,8)$, the loops are non-simple and may touch each other and the boundary. As a second application, we derive the probability that the loop surrounding a given point in the non-simple conformal loop ensemble touches the domain boundary.
Date: Tuesday, April 23, 2024 | 1:00pm | Room: 4-265
Committee: Wei Zhang (advisor/chair), Julee Kim, Spencer Leslie (Boston College)
Twisted Gan-Gross-Prasad conjecture for unramified quadratic extensions
The global twisted GGP conjecture is a variant of the Gan-Gross-Prasad conjecture for unitary groups, which considers the restriction of an automorphic representation of GL(V) to its subgroup U(V), for a skew-Hermitian space V. It relates the nonvanishing of a certain period integral to the central value of an L-function attached to the representation.
Date: Tuesday, April 30, 2024 | 3:30pm | Room: 2-255 | Zoom Link
Committee: Scott Sheffield (thesis advisor), Alexei Borodin, Curtis McMullen
Random geometry in two and three dimensions
A central theme in random geometry is the interplay between discrete models and continuum ones that appear in scaling limits. Surprising structure and symmetry often arises in these scaling limits, leading to an interplay between combinatorics, probability, complex analysis, and geometry.
The dimer model is one of the classical lattice models of statistical mechanics and can be defined in any dimension. In the first half of this thesis, we prove a large deviation principle for dimer tilings in three dimensions. This generalizes a two-dimensional result of Cohn, Kenyon, and Propp, and is one of the first results for dimers in any dimension $d>2$. Many ideas and constructions used to study dimers are specific to two dimensions, so our arguments start from a smaller set of tools including Hall's matching theorem, the qualitative description of the Gibbs property, and a double dimer swapping operation.
In the second half of this thesis, we study discrete, geometrically-motivated coordinates called shears on the space of circle homeomorphisms up to M\"obius transformations. The Weil-Petersson Teichm\"uller space is a subspace of this which has been of long-term interest in geometry and string theory and has recent connections to SLE curves in probability. We introduce and study natural $\ell^2$ spaces in terms of shears, and obtain sharp results comparing them to H\"older classes of circle homeomorphisms and the Weil-Petersson class. We also give some preliminary results about i.i.d. Gaussian random shears.
Home > USC Columbia > Arts and Sciences > Mathematics > Mathematics Theses and Dissertations
Theses/dissertations from 2023 2023.
Extreme Covering Systems, Primes Plus Squarefrees, and Lattice Points Close to a Helix , Jack Robert Dalton
On the Algebraic and Geometric Multiplicity of Zero as a Hypergraph Eigenvalue , Grant Ian Fickes
Deep Learning for Studying Materials Stability and Solving Thermodynamically Consistent PDES With Dynamic Boundary Conditions in Arbitrary Domains , Chunyan Li
Widely Digitally Delicate Brier Primes and Irreducibility Results for Some Classes of Polynomials , Thomas David Luckner
Deep Learning Methods for Some Problems in Scientific Computing , Yuankai Teng
Covering Systems and the Minimum Modulus Problem , Maria Claire Cummings
The Existence and Quantum Approximation of Optimal Pure State Ensembles , Ryan Thomas McGaha
Structure Preserving Reduced-Order Models of Hamiltonian Systems , Megan Alice McKay
Tangled up in Tanglegrams , Drew Joseph Scalzo
Results on Select Combinatorial Problems With an Extremal Nature , Stephen Smith
Poset Ramsey Numbers for Boolean Lattices , Joshua Cain Thompson
Some Properties and Applications of Spaces of Modular Forms With ETA-Multiplier , Cuyler Daniel Warnock
Simulation of Pituitary Organogenesis in Two Dimensions , Chace E. Covington
Polynomials, Primes and the PTE Problem , Joseph C. Foster
Widely Digitally Stable Numbers and Irreducibility Criteria For Polynomials With Prime Values , Jacob Juillerat
A Numerical Investigation of Fractional Models for Viscoelastic Materials With Applications on Concrete Subjected to Extreme Temperatures , Murray Macnamara
Trimming Complexes , Keller VandeBogert
Multiple Frailty Model for Spatially Correlated Interval-Censored , Wanfang Zhang
An Equivariant Count of Nodal Orbits in an Invariant Pencil of Conics , Candace Bethea
Finite Axiomatisability in Nilpotent Varieties , Joshua Thomas Grice
Rationality Questions and the Derived Category , Alicia Lamarche
Counting Number Fields by Discriminant , Harsh Mehta
Distance Related Graph Invariants in Triangulations and Quadrangulations of the Sphere , Trevor Vincent Olsen
Diameter of 3-Colorable Graphs and Some Remarks on the Midrange Crossing Constant , Inne Singgih
Two Inquiries Related to the Digits of Prime Numbers , Jeremiah T. Southwick
Windows and Generalized Drinfeld Kernels , Robert R. Vandermolen
Connections Between Extremal Combinatorics, Probabilistic Methods, Ricci Curvature of Graphs, and Linear Algebra , Zhiyu Wang
An Ensemble-Based Projection Method and Its Numerical Investigation , Shuai Yuan
Variable-Order Fractional Partial Differential Equations: Analysis, Approximation and Inverse Problem , Xiangcheng Zheng
Classification of Non-Singular Cubic Surfaces up to e-invariants , Mohammed Alabbood
On the Characteristic Polynomial of a Hypergraph , Gregory J. Clark
A Development of Transfer Entropy in Continuous-Time , Christopher David Edgar
Moving Off Collections and Their Applications, in Particular to Function Spaces , Aaron Fowlkes
Finding Resolutions of Mononomial Ideals , Hannah Melissa Kimbrell
Regression for Pooled Testing Data with Biomedical Applications , Juexin Lin
Numerical Methods for a Class of Reaction-Diffusion Equations With Free Boundaries , Shuang Liu
An Implementation of the Kapustin-Li Formula , Jessica Otis
A Nonlinear Parallel Model for Reversible Polymer Solutions in Steady and Oscillating Shear Flow , Erik Tracey Palmer
A Few Problems on the Steiner Distance and Crossing Number of Graphs , Josiah Reiswig
Successful Pressing Sequences in Simple Pseudo-Graphs , Hays Wimsatt Whitlatch
On The Generators of Quantum Dynamical Semigroups , Alexander Wiedemann
An Examination of Kinetic Monte Carlo Methods with Application to a Model of Epitaxial Growth , Dylana Ashton Wilhelm
Dynamical Entropy of Quantum Random Walks , Duncan Wright
Unconditionally Energy Stable Linear Schemes for a Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State , Chenfei Zhang
Theory, Computation, and Modeling of Cancerous Systems , Sameed Ahmed
Turán Problems and Spectral Theory on Hypergraphs and Tensors , Shuliang Bai
Quick Trips: On the Oriented Diameter of Graphs , Garner Paul Cochran
Geometry of Derived Categories on Noncommutative Projective Schemes , Blake Alexander Farman
A Quest for Positive Definite Matrices over Finite Fields , Erin Patricia Hanna
Comparison of the Performance of Simple Linear Regression and Quantile Regression with Non-Normal Data: A Simulation Study , Marjorie Howard
Special Fiber Rings of Certain Height Four Gorenstein Ideals , Jaree Hudson
Graph Homomorphisms and Vector Colorings , Michael Robert Levet
Local Rings and Golod Homomorphisms , Thomas Schnibben
States and the Numerical Range in the Regular Algebra , James Patrick Sweeney
Thermodynamically Consistent Hydrodynamic Phase Field Models and Numerical Approximation for Multi-Component Compressible Viscous Fluid Mixtures , Xueping Zhao
On the Existence of Non-Free Totally Reflexive Modules , J. Cameron Atkins
Subdivision of Measures of Squares , Dylan Bates
Unconditionally Energy Stable Numerical Schemes for Hydrodynamics Coupled Fluids Systems , Alexander Yuryevich Brylev
Convergence and Rate of Convergence of Approximate Greedy-Type Algorithms , Anton Dereventsov
Covering Subsets of the Integers and a Result on Digits of Fibonacci Numbers , Wilson Andrew Harvey
Nonequispaced Fast Fourier Transform , David Hughey
Deep Learning: An Exposition , Ryan Kingery
A Family of Simple Codimension Two Singularities with Infinite Cohen-Macaulay Representation Type , Tyler Lewis
Polynomials Of Small Mahler Measure With no Newman Multiples , Spencer Victoria Saunders
On Crown-free Set Families, Diffusion State Difference, and Non-uniform Hypergraphs , Edward Lawrence Boehnlein
Structure of the Stable Marriage and Stable Roommate Problems and Applications , Joe Hidakatsu
Binary Quartic Forms over Fp , Daniel Thomas Kamenetsky
On a Constant Associated with the Prouhet-Tarry-Escott Problem , Maria E. Markovich
Some Extremal And Structural Problems In Graph Theory , Taylor Mitchell Short
Chebyshev Inversion of the Radon Transform , Jared Cameron Szi
Modeling of Structural Relaxation By A Variable-Order Fractional Differential Equation , Su Yang
Modeling, Simulation, and Applications of Fractional Partial Differential Equations , Wilson Cheung
The Packing Chromatic Number of Random d-regular Graphs , Ann Wells Clifton
Commutator Studies in Pursuit of Finite Basis Results , Nathan E. Faulkner
Avoiding Doubled Words in Strings of Symbols , Michael Lane
A Survey of the Kinetic Monte Carlo Algorithm as Applied to a Multicellular System , Michael Richard Laughlin
Toward the Combinatorial Limit Theory of free Words , Danny Rorabaugh
Trees, Partitions, and Other Combinatorial Structures , Heather Christina Smith
Fast Methods for Variable-Coefficient Peridynamic and Non-Local Diffusion Models , Che Wang
Modeling and Computations of Cellular Dynamics Using Complex-fluid Models , Jia Zhao
The Non-Existence of a Covering System with all Moduli Distinct, Large and Square-Free , Melissa Kate Bechard
Explorations in Elementary and Analytic Number Theory , Scott Michael Dunn
Independence Polynomials , Gregory Matthew Ferrin
Turán Problems on Non-uniform Hypergraphs , Jeremy Travis Johnston
On the Group of Transvections of ADE-Diagrams , Marvin Jones
Fake Real Quadratic Orders , Richard Michael Oh
Shimura Images of A Family of Half-Integral Weight Modular Forms , Kenneth Allan Brown
Sharp Bounds Associated With An Irreducibility Theorem For Polynomials Having Non-Negative Coefficients , Morgan Cole
Deducing Vertex Weights From Empirical Occupation Times , David Collins
Analysis and Processing of Irregularly Distributed Point Clouds , Kamala Hunt Diefenthaler
Generalizations of Sperner's Theorem: Packing Posets, Families Forbidding Posets, and Supersaturation , Andrew Philip Dove
Spectral Analysis of Randomly Generated Networks With Prescribed Degree Sequences , Clifford Davis Gaddy
Selected Research In Covering Systems of the Integers and the Factorization of Polynomials , Joshua Harrington
The Weierstrass Approximation Theorem , LaRita Barnwell Hipp
The Compact Implicit Integration Factor Scheme For the Solution of Allen-Cahn Equations , Meshack K. Kiplagat
Applications of the Lopsided Lovász Local Lemma Regarding Hypergraphs , Austin Tyler Mohr
Study On Covolume-Upwind Finite Volume Approximations For Linear Parabolic Partial Differential Equations , Rosalia Tatano
Coloring Pythagorean Triples and a Problem Concerning Cyclotomic Polynomials , Daniel White
A Computational Approach to the Quillen-Suslin Theorem, Buchsbaum-Eisenbud Matrices, and Generic Hilbert-Burch Matrices , Jonathan Brett Barwick
Mathematical Modeling and Computational Studies for Cell Signaling , Kanadpriya Basu
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Could any one recommend some comprehensive guide (online version preferred) for writing a Ph.D. thesis in Mathematics?
I did some google search but there are too many results and it is difficult to decide which one to read. Here I am not asking anyone to write such a guide for me (otherwise this question will be too broad and thus not suitable here); instead, I would appreciate if anyone could make some recommendations of those existing references.
It could also be helpful to check this and this short guides and the books by Steven G. Krantz, in particular
The first one contains subsection 4.6 which deals specifically with writing a thesis, the second one is on mathematical writing in general but it does not really deal with the theses per se .
This is the best guide I have ever encountered.
It is neither too broad nor too narrow as a guide. Moreover, it does not contain the policies of a specific university (you should number the figures that way and write equations this way etc.)
The persentation explains how should the overall feeling of a thesis be, and nothing more.
I also find this manuscript very useful. However, some subsections are incomplete and marked as [todo] .
Not the answer you're looking for browse other questions tagged phd thesis mathematics reference-request ..
Doctoral theses.
About twenty to thirty doctoral students complete their doctoral thesis at the Department of Mathematics every year.
Recent doctoral examinations
Published after 1 January 2014. For theses published before 2014, please refer to the Research Collection .
Home > Computational, Mathematical, and Physical Sciences > Mathematics Education > Theses and Dissertations
Theses/dissertations from 2024 2024.
Rigorous Verification of Stability of Ideal Gas Layers , Damian Anderson
Documentation of Norm Negotiation in a Secondary Mathematics Classroom , Michelle R. Bagley
New Mathematics Teachers' Goals, Orientations, and Resources that Influence Implementation of Principles Learned in Brigham Young University's Teacher Preparation Program , Caroline S. Gneiting
Impact of Applying Visual Design Principles to Boardwork in a Mathematics Classroom , Jennifer Rose Canizales
Practicing Mathematics Teachers' Perspectives of Public Records in Their Classrooms , Sini Nicole White Graff
Parents' Perceptions of the Importance of Teaching Mathematics: A Q-Study , Ashlynn M. Holley
Engagement in Secondary Mathematics Group Work: A Student Perspective , Rachel H. Jorgenson
Understanding College Students' Use of Written Feedback in Mathematics , Erin Loraine Carroll
Identity Work to Teach Mathematics for Social Justice , Navy B. Dixon
Developing a Quantitative Understanding of U-Substitution in First-Semester Calculus , Leilani Camille Heaton Fonbuena
The Perception of At-Risk Students on Caring Student-Teacher Relationships and Its Impact on Their Productive Disposition , Brittany Hopper
Variational and Covariational Reasoning of Students with Disabilities , Lauren Rigby
Structural Reasoning with Rational Expressions , Dana Steinhorst
Student-Created Learning Objects for Mathematics Renewable Assignments: The Potential Value They Bring to the Broader Community , Webster Wong
Emotional Geographies of Beginning and Veteran Reformed Teachers in Mentor/Mentee Relationships , Emily Joan Adams
You Do Math Like a Girl: How Women Reason Mathematically Outside of Formal and School Mathematics Contexts , Katelyn C. Pyfer
Developing the Definite Integral and Accumulation Function Through Adding Up Pieces: A Hypothetical Learning Trajectory , Brinley Nichole Stevens
Mathematical Identities of Students with Mathematics Learning Dis/abilities , Emma Lynn Holdaway
Teachers' Mathematical Meanings: Decisions for Teaching Geometric Reflections and Orientation of Figures , Porter Peterson Nielsen
Student Use of Mathematical Content Knowledge During Proof Production , Chelsey Lynn Van de Merwe
Making Sense of the Equal Sign in Middle School Mathematics , Chelsea Lynn Dickson
Developing Understanding of the Chain Rule, Implicit Differentiation, and Related Rates: Towards a Hypothetical Learning Trajectory Rooted in Nested Multivariation , Haley Paige Jeppson
Secondary Preservice Mathematics Teachers' Curricular Reasoning , Kimber Anne Mathis
“Don’t Say Gay. We Say Dumb or Stupid”: Queering ProspectiveMathematics Teachers’ Discussions , Amy Saunders Ross
Aspects of Engaging Problem Contexts From Students' Perspectives , Tamara Kay Stark
Addressing Pre-Service Teachers' Misconceptions About Confidence Intervals , Kiya Lynn Eliason
How Teacher Questions Affect the Development of a Potential Hybrid Space in a Classroom with Latina/o Students , Casandra Helen Job
Teacher Graphing Practices for Linear Functions in a Covariation-Based College Algebra Classroom , Konda Jo Luckau
Principles of Productivity Revealed from Secondary Mathematics Teachers' Discussions Around the Productiveness of Teacher Moves in Response to Teachable Moments , Kylie Victoria Palsky
Curriculum Decisions and Reasoning of Middle School Teachers , Anand Mikel Bernard
Teacher Response to Instances of Student Thinking During Whole Class Discussion , Rachel Marie Bernard
Kyozaikenkyu: An In-Depth Look into Japanese Educators' Daily Planning Practices , Matthew David Melville
Analysis of Differential Equations Applications from the Coordination Class Perspective , Omar Antonio Naranjo Mayorga
The Principles of Effective Teaching Student Teachershave the Opportunity to Learn in an AlternativeStudent Teaching Structure , Danielle Rose Divis
Insight into Student Conceptions of Proof , Steven Daniel Lauzon
Teacher Participation and Motivation inProfessional Development , Krystal A. Hill
Student Evaluation of Mathematical Explanations in anInquiry-Based Mathematics Classroom , Ashley Burgess Hulet
English Learners' Participation in Mathematical Discourse , Lindsay Marie Merrill
Mathematical Interactions between Teachers and Students in the Finnish Mathematics Classroom , Paula Jeffery Prestwich
Parents and the Common Core State Standards for Mathematics , Rebecca Anne Roberts
Examining the Effects of College Algebra on Students' Mathematical Dispositions , Kevin Lee Watson
Problems Faced by Reform Oriented Novice Mathematics Teachers Utilizing a Traditional Curriculum , Tyler Joseph Winiecke
Academic and Peer Status in the Mathematical Life Stories of Students , Carol Ann Wise
The Effect of Students' Mathematical Beliefs on Knowledge Transfer , Kristen Adams
Language Use in Mathematics Textbooks Written in English and Spanish , Kailie Ann Bertoch
Teachers' Curricular Reasoning and MKT in the Context of Algebra and Statistics , Kolby J. Gadd
Mathematical Telling in the Context of Teacher Interventions with Collaborative Groups , Brandon Kyle Singleton
An Investigation of How Preservice Teachers Design Mathematical Tasks , Elizabeth Karen Zwahlen
Student Understanding of Limit and Continuity at a Point: A Look into Four Potentially Problematic Conceptions , Miriam Lynne Amatangelo
Exploring the Mathematical Knowledge for Teaching of Japanese Teachers , Ratu Jared R. T. Bukarau
Comparing Two Different Student Teaching Structures by Analyzing Conversations Between Student Teachers and Their Cooperating Teachers , Niccole Suzette Franc
Professional Development as a Community of Practice and Its Associated Influence on the Induction of a Beginning Mathematics Teacher , Savannah O. Steele
Types of Questions that Comprise a Teacher's Questioning Discourse in a Conceptually-Oriented Classroom , Keilani Stolk
Student Teachers' Interactive Decisions with Respect to Student Mathematics Thinking , Jonathan J. Call
Manipulatives and the Growth of Mathematical Understanding , Stacie Joyce Gibbons
Learning Within a Computer-Assisted Instructional Environment: Effects on Multiplication Math Fact Mastery and Self-Efficacy in Elementary-Age Students , Loraine Jones Hanson
Mathematics Teacher Time Allocation , Ashley Martin Jones
How Student Positioning Can Lead to Failure in Inquiry-based Classrooms , Kelly Beatrice Campbell
Teachers' Decisions to Use Student Input During Class Discussion , Heather Taylor Toponce
A Conceptual Framework for Student Understanding of Logarithms , Heather Rebecca Ambler Williams
Growth in Students' Conceptions of Mathematical Induction , John David Gruver
Contextualized Motivation Theory (CMT): Intellectual Passion, Mathematical Need, Social Responsibility, and Personal Agency in Learning Mathematics , Janelle Marie Hart
Thinking on the Brink: Facilitating Student Teachers' Learning Through In-the-Moment Interjections , Travis L. Lemon
Understanding Teachers' Change Towards a Reform-Oriented Mathematics Classroom , Linnae Denise Williams
A Comparison of Mathematical Discourse in Online and Face-to-Face Environments , Shawn D. Broderick
The Influence of Risk Taking on Student Creation of Mathematical Meaning: Contextual Risk Theory , Erin Nicole Houghtaling
Uncovering Transformative Experiences: A Case Study of the Transformations Made by one Teacher in a Mathematics Professional Development Program , Rachelle Myler Orsak
Student Teacher Knowledge and Its Impact on Task Design , Tenille Cannon
How Eighth-Grade Students Estimate with Fractions , Audrey Linford Hanks
Similar but Different: The Complexities of Students' Mathematical Identities , Diane Skillicorn Hill
Choose Your Words: Refining What Counts as Mathematical Discourse in Students' Negotiation of Meaning for Rate of Change of Volume , Christine Johnson
Mathematics Student Teaching in Japan: A Multi-Case Study , Allison Turley Shwalb
Applying Toulmin's Argumentation Framework to Explanations in a Reform Oriented Mathematics Class , Jennifer Alder Brinkerhoff
What Are Some of the Common Traits in the Thought Processes of Undergraduate Students Capable of Creating Proof? , Karen Malina Duff
Probing for Reasons: Presentations, Questions, Phases , Kellyn Nicole Farlow
One Problem, Two Contexts , Danielle L. Gigger
The Main Challenges that a Teacher-in-Transition Faces When Teaching a High School Geometry Class , Greg Brough Henry
Discovering the Derivative Can Be "Invigorating:" Mark's Journey to Understanding Instantaneous Velocity , Charity Ann Gardner Hyer
How a Master Teacher Uses Questioning Within a Mathematical Discourse Community , Omel Angel Contreras
Determining High School Geometry Students' Geometric Understanding Using van Hiele Levels: Is There a Difference Between Standards-based Curriculum Students and NonStandards-based Curriculum Students? , Rebekah Loraine Genz
The Nature and Frequency of Mathematical Discussion During Lesson Study That Implemented the CMI Framework , Andrew Ray Glaze
Second Graders' Solution Strategies and Understanding of a Combination Problem , Tiffany Marie Hessing
What Does It Mean To Preservice Mathematics Teachers To Anticipate Student Responses? , Matthew M. Webb
Fraction Multiplication and Division Image Change in Pre-Service Elementary Teachers , Jennifer J. Cluff
An Examination of the Role of Writing in Mathematics Instruction , Amy Jeppsen
Reasoning About Motion: A Case Study , Tiffini Lynn Glaze
An Analysis of the Influence of Lesson Study on Preservice Secondary Mathematics Teachers' View of Self-As Mathematics Expert , Julie Stafford
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A selection of Mathematics PhD thesis titles is listed below, some of which are available online: 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991. 2024. Reham Alahmadi - Asymptotic Study of Toeplitz Determinants with Fisher-Hartwig Symbols and Their Double-Scaling Limits
In 1909 the department awarded its first PhD to Grace M. Bareis, whose dissertation was directed by Professor Harry W. Kuhn.The department began awarding PhD degrees on a regular basis around 1930, when a formal doctoral program was established as a result of the appointment of Tibor Radó as a professor at our department. To date, the department has awarded over 800 PhD degrees.
Many older dissertations can be found on ProQuest Dissertation and Theses Search which many university libraries subscribe to. Harvard University. Department of Mathematics. Science Center Room 325. 1 Oxford Street. Cambridge, MA 02138 USA. Tel: (617) 495-2171 Fax: (617) 495-5132. Department Main Office Contact.
Recent PhD Theses Inside Graduate Admissions. Prospective Graduate Student FAQ; PhD Requirements. Graduate Board Oral Exam; Graduate Courses; Qualifying Exams; ... Department of Mathematics. Johns Hopkins University 404 Krieger Hall 3400 N. Charles Street Baltimore, MD 21218. Contact Us. [email protected]. 410-516-7397.
Below is a list of PhD dissertations written by students at the Harvard Department of Mathematics. All scholars can order copies of most Harvard dissertations from 1982 to the present by contacting UMI/ProQuest at 1-800-521-3042. Permission of the author is usually required to copy theses within the last five years.
Modeling and simulation of uni- and multi-flagellar bacterial locomotion in a viscous fluid. PhD Theses 2022. Author. Title. James Petrie. Decentralized contact tracing protocols and a risk analysis approach to pandemic control. Yiming Meng. Bifurcation and Robust Control of Instabilities in the Presence of Uncertainties.
Indicators of Future Mathematics Proficiency: Literature Review & Synthesis, Claudia Preciado PDF Ádám's Conjecture and Arc Reversal Problems , Claudio D. Salas
For PhD Thesis, see here.This page is about Senior thesis. In order that senior thesis produced by Harvard math students are easier for other undergrads to benefit from, we would like to exhibit more senior theses online (while all theses are available through Harvard university archives, it would be more convenient to have them online).It is absolutely voluntary, but if you decide to give us ...
Estimation and application of Bayesian Hawkes process models . Deutsch, Isabella (The University of Edinburgh, 2024-03-13) In this thesis, we examine various facets of Bayesian approaches to Hawkes Processes. Hawkes Processes are a flexible class of point processes that are used to model events that occur in clusters or bursts, as classic ...
Numerical Streamline Methods for Solving Steady Flow Problems (Methods, Compressible, Free Surface, Finite Difference.) Jie Sun. On Monotropic Piecewise Quadratic Programming (Network, Algorithm, Convex Programming, Decomposition Method.) Name Dissertation Title Advising Professor (s) 2022 Yuying Liu.
Advisor: Daniel Halpern-Leistner. First Position: Postdoc at the Institution for Advanced Study and Princeton. Max Lipton. Thesis: Dynamical Systems in Pure Mathematics. Advisor: Steven Strogatz. First Position: NSF Mathematical Sciences Postdoctoral Fellow at Massachusetts Institute of Technology. Elise McMahon.
Al Kohli, Raad Sameer Al Sheikh (2024-06-11) - Thesis. In this thesis we shall study classes of groups defined by formal languages. Our first main topic is the class of groups defined by having an ET0L co-word problem; i.e., the class of co-ET0L groups.
Columbia University. Department of Mathematics. Recent Doctoral Theses. The Gauss curvature flow: regularity and asymptotic behavior Kyeongsu Choi, May 2017 (Advisor: P. Daskalopoulos) Tropical geometry of curves with large theta characteristics Ashwin Deopurkar, May 2017 (Advisor: J. de Jong) Linear stability of Schwarzschild spacetime Jordan ...
Dissertations. Here is the complete list of all doctoral dissertations granted by the School of Math, which dates back to 1965. Included below are also all masters theses produced by our students since 2002. A combined listing of all dissertations and theses, going back to 1934, is available at Georgia Tech's library archive.
Course Information Recent PhDs Thesis Abstracts Papers, Presentations, and Posters. The following PhD theses abstracts are available in .pdf format. To see where these students have taken jobs, see the list of recent graduates. 2024. On Pattern Avoidance and Dynamical Algebraic Combinatorics - Ben Adenbaum.
2003. David Seida. Janos Turi. Estimation of Attitude Parameters from Variation in Image Overlap. 2002. Kathryn Flores. Viswanath Ramakrishna. Classical and Quantum Controls from Decomposition of Unitary Matrices. See a list of PhD Dissertations in Mathematics over the last 20 years at The University of Texas at Dallas.
This PhD thesis is divided in two parts. The first part consists on the self-similar singularity formation for the compressible Euler equation and its applications. ... Department of Mathematics Headquarters Office Simons Building (Building 2), Room 106 77 Massachusetts Avenue Cambridge, MA 02139-4307 Campus Map (617) 253-4381. Website ...
Theses/Dissertations from 2022. PDF. Covering Systems and the Minimum Modulus Problem, Maria Claire Cummings. PDF. The Existence and Quantum Approximation of Optimal Pure State Ensembles, Ryan Thomas McGaha. PDF. Structure Preserving Reduced-Order Models of Hamiltonian Systems, Megan Alice McKay. PDF.
A Mathematician's Survival Guide: Graduate School and Early Career Development. A Primer of Mathematical Writing. The first one contains subsection 4.6 which deals specifically with writing a thesis, the second one is on mathematical writing in general but it does not really deal with the theses per se. Share.
About twenty to thirty doctoral students complete their doctoral thesis at the Department of Mathematics every year. Recent doctoral examinations. Dissertations. Published after 1 January 2014. ... Tim De Ryck: 2023 Analytics Club PhD Award; Doctoral exam of Paula Truöl; Doctoral exam of Laurin Köhler-Schindler; Discover, solve puzzles, find ...
Theses/Dissertations from 2020. Mathematical Identities of Students with Mathematics Learning Dis/abilities, Emma Lynn Holdaway. Teachers' Mathematical Meanings: Decisions for Teaching Geometric Reflections and Orientation of Figures, Porter Peterson Nielsen. Student Use of Mathematical Content Knowledge During Proof Production, Chelsey Lynn ...
For Ph.D. Theses, see here. A senior thesis is required by the Mathematics concentration to be a candidate for graduation with the distinction of High or Highest honors in Mathematics. See the document ' Honors in Mathematics ' for more information about honors recommendations and about finding a topic and advisor for your thesis.
The incoming graduate students are advised by the Director of Graduate Studies of the Mathematics Department. The Director, in consultation with the students, determines appropriate first-year courses for each student, according to their preparation and interests. ... program is a professional, non-thesis degree that is jointly offered by the ...
Graduate; Masters Theses. Author, Title, or Publisher ... Department of Mathematics University of Washington Administrative Office C-138 Padelford Box 354350 Seattle, WA 98195-4350 Phone: (206) 543-1150 Fax: (206) 543-0397. For all academic inquiries, please contact: Math Student Services