Dissertations

2017

Theodore HuiA radical characterization of abelian varieties
Advisor: 
David Zywina
Daniel MillerCounterexamples related to the Sato–Tate conjecture
Advisor: 
Ravi Ramakrishna
Lihai QianRigidity on Einstein manifolds and shrinking Ricci solitons in high dimensions
Advisor: 
Xiaodong Cao
Valente Ramirez Garcia LunaQuadratic vector fields on the complex plane: rigidity and analytic invariants
Advisor: 
Yulij Ilyashenko
Iian SmytheSet theory in infinite-dimensional vector spaces
Advisor: 
Justin Moore
Zhexiu TuTopological representations of matroids and the cd-index
Advisor: 
Edward Swartz
Wai-kit YeungRepresentation homology and knot contact homology
Advisor: 
Yuri Berest

2016

Lucien ClavierNon-affine horocycle orbit closures on strata of translation surfaces: new examples
Advisor: 
John Smillie
Voula CollinsCrystal branching for non-Levi subgroups and a puzzle formula for the equivariant cohomology of the cotangent bundle on projective space
Advisor: 
Allen Knutson
Pok Wai FongSmoothness Properties of symbols, Calderón Commutators and Generalizations
Advisor: 
Camil Muscalu
Tom KernNonstandard models of the weak second order theory of one successor
Advisor: 
Anil Nerode
Robert KeslerUnbounded multilinear multipliers adapted to large subspaces and estimates for degenerate simplex operators
Advisor: 
Camil Muscalu
Yao LiuRiesz Distributions Assiciated to Dunkl Operators
Advisor: 
Yuri Berest
Scott MessickContinuous atomata, compactness, and Young measures
Advisor: 
Anil Nerode
Aaron PalmerIncompressibility and Global Injectivity in Second-Gradient Non-Linear Elasticity
Advisor: 
Timothy J. Healey
Kristen PueschelOn Residual Properties of Groups and Dehn Functions for Mapping Tori of Right Angled Artin Groups
Advisor: 
Timothy Riley
Chenxi WuTRANSLATION SURFACES: SADDLE CONNECTIONS, TRIANGLES AND COVERING CONSTRUCTIONS
Advisor: 
John Smillie

2015

David BelangerSets, Models, And Proofs: Topics In The Theory Of Recursive Functions
Advisor: 
Richard A. Shore
Cristina BeneaVector-Valued Extensions for Singular Bilinear Operators and Applications
Advisor: 
Camil Muscalu
Kai Fong Ernest ChongFace Vectors and Hilbert Functions
Advisor: 
Edward Swartz
Laura Escobar VegaBrick Varieties and Toric Matrix Schubert Varieties
Advisor: 
Allen Knutson
Joeun JungIterated trilinear fourier integrals with arbitrary symbols
Advisor: 
Camil Muscalu
Yasemin KaraThe laplacian on hyperbolic Riemann surfaces and Maass forms
Advisor: 
John H. Hubbard
Chor Hang LamHomological Stability Of Diffeomorphism Groups Of 3-Manifolds
Advisor: 
Allen Hatcher
Yash LodhaFiniteness Properties And Piecewise Projective Homeomorphisms
Advisor: 
Justin Moore
Timothy Riley
Radoslav ZlatevExamples of Implicitization of Hypersurfaces through Syzygies
Advisor: 
Michael E. Stillman

2014

Margarita AmchislavskaThe geometry of generalized Lamplighter groups
Advisor: 
Timothy Riley
Hyungryul BaikLaminations on the circle and hyperbolic geometry
Advisor: 
John H. Hubbard
Adam BjorndahlLanguage-based games
Advisor: 
Anil Nerode
Joseph Halpern
Youssef El Fassy FihryGraded Cherednik Algebra And Quasi-Invariant Differential Forms
Advisor: 
Yuri Berest
Chikwong FokThe Real K-theory of compact Lie groups
Advisor: 
Reyer Sjamaar
Kathryn LindseyFamilies Of Dynamical Systems Associated To Translation Surfaces
Advisor: 
John Smillie
Andrew MarshallOn configuration spaces of graphs
Advisor: 
Allan Hatcher
Robyn MillerSymbolic Dynamics Of Billiard Flow In Isosceles Triangles
Advisor: 
John Smillie
Diana Ojeda AristizabalRamsey theory and the geometry of Banach spaces
Advisor: 
Justin Moore
Hung TranAspects of the Ricci flow
Advisor: 
Xiaodong Cao
Baris Ugurcan$L^P$-Estimates And Polyharmonic Boundary Value Problems On The Sierpinski Gasket And Gaussian Free Fields On High Dimensional Sierpinski Carpet Graphs
Advisor: 
Robert S. Strichartz

2013

Anna BertigerThe Combinatorics and Geometry of the Orbits of the Symplectic Group on Flags in Complex Affine Space
Advisor: 
Allen Knutson
Mariya BessonovProbabilistic Models for Population Dynamics
Advisor: 
Richard Durrett
Igors GorbovickisSome Problems from Complex Dynamical Systems and Combinatorial Geometry
Advisor: 
Yulij Ilyashenko
Marisa HughesQuotients of Spheres by Linear Actions of Abelian Groups
Advisor: 
Edward Swartz
Kristine JonesGeneric Initial Ideals of Locally Cohen-Macaulay Space Curves
Advisor: 
Michael E. Stillman
Shisen LuoHard Lefschetz Property of Hamiltonian GKM Manifolds
Advisor: 
Tara Holm
Peter LuthyBi-parameter Maximal Multilinear Operators
Advisor: 
Camil Muscalu
Remus RaduTopological models for hyperbolic and semi-parabolic complex Hénon maps
Advisor: 
John H. Hubbard
Jenna RajchgotCompatibly Split Subvarieties of the Hilbert Scheme of Points in the Plane
Advisor: 
Allen Knutson
Raluca TanaseHénon maps, discrete groups and continuity of Julia sets
Advisor: 
John H. Hubbard
Ka Yue WongDixmier Algebras on Complex Classical Nilpotent Orbits and their Representation Theories
Advisor: 
Dan M. Barbasch
Tianyi ZhengRandom walks on some classes of solvable groups
Advisor: 
Laurent Saloff-Coste

2012

Juan AlonsoGraphs of Free Groups and their Measure Equivalence
Advisor: 
Karen Vogtmann
Jason AnemaCounting Spanning Trees on Fractal Graphs
Advisor: 
Robert S. Strichartz
Saúl Blanco RodríguezShortest Path Poset of Bruhat Intervals and the Completecd-Index
Advisor: 
Louis Billera
Fatima MahmoodJacobi Structures and Differential Forms on Contact Quotients
Advisor: 
Reyer Sjamaar
Philipp MeerkampSingular Hopf Bifurcation
Advisor: 
John M. Guckenheimer
Milena PabiniakHamiltonian Torus Actions in Equivariant Cohomology and Symplectic Topology
Advisor: 
Tara Holm
Peter SamuelsonKauffman Bracket Skein Modules and the Quantum Torus
Advisor: 
Yuri Berest

2011

Mihai Bailesteanu The Heat Equation under the Ricci Flow
Advisor: 
Xiaodong Cao
Owen Baker The Jacobian Map on Outer Space
Advisor: 
Karen Vogtmann
Jennifer Biermann Free Resolutions of Monomial Ideals
Advisor: 
Irena Peeva
Mingzhong Cai Elements of Classical Recursion Theory: Degree-Theoretic Properties and Combinatorial Properties
Advisor: 
Richard A. Shore
Ri-Xiang Chen Hilbert Functions and Free Resolutions
Advisor: 
Irena Peeva
Denise Dawson Complete Reducibility in Euclidean Twin Buildings
Advisor: 
Kenneth S. Brown
George KhachatryanDerived Representation Schemes and Non-commutative Geometry
Advisor: 
Yuri Berest
Samuel Kolins Face Vectors of Subdivision of Balls
Advisor: 
Edward Swartz
Victor KostyukOuter Space for Two-Dimensional RAAGs and Fixed Point Sets of Finite Subgroups
Advisor: 
Karen Vogtmann
Ho Hon Leung K-Theory of Weight Varieties and Divided Difference Operators in Equivariant KK-Theory
Advisor: 
Reyer Sjamaar
Benjamin Lundell Selmer Groups and Ranks of Hecke Rings
Advisor: 
Ravi Ramakrishna
Eyvindur Ari Palsson Lp Estimates for a Singular Integral Operator Motivated by Calderón’s Second Commutator
Advisor: 
Camil Muscalu
Paul Shafer On the Complexity of Mathematical Problems: Medvedev Degrees and Reverse Mathematics
Advisor: 
Richard A. Shore
Michelle Snider Affine Patches on Positroid Varieties and Affine Pipe Dreams
Advisor: 
Allen Knutson
Santi TasenaHeat Kernel Analysis on Weighted Dirichlet Spaces
Advisor: 
Laurent Saloff-Coste
Russ Thompson Random Walks and Subgroup Geometry
Advisor: 
Laurent Saloff-Coste
Gwyneth WhieldonBetti Numbers of Stanley-Reisner Ideals
Advisor: 
Michael E. Stillman

2010

Andrew CameronEstimates 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
Timothy GoldbergHamiltonian Actions in Integral Kähler and Generalized Complex Geometry
Advisor: 
Reyer Sjamaar
Gregory MullerThe Projective Geometry of Differential Operators
Advisor: 
Yuri Berest
Matthew NoonanGeometric Backlund transofrmation in homogeneous spaces
Advisor: 
John H. Hubbard
Sergio Pulido NiñoFinancial Markets with Short Sales Prohibition
Advisor: 
Philip E. Protter

2009

Joshua BowmanFlat Structures and Complex Structures in Teichmüller Theory
Advisor: 
John H. Hubbard
Nikolai DimitrovRapid Evolution of Complex Limit Cycles
Advisor: 
Yulij Ilyashenko
Alimjon EshmatovGroup-Valued Implosion and Conjugation Spaces
Advisor: 
Reyer Sjamaar
Bradley ForrestDegree Subcomplexes of Auter Space and Ribbon Graph Complexes
Advisor: 
Karen Vogtmann
Chris LipaMonodromy and Hénon Mappings
Advisor: 
John H. Hubbard
Radu MurgescuOn the p-Class Groups of the Pure Number Field Q(N1/p) and its Galois Closure Q(N1/p, ζp)
Advisor: 
Ravi Ramakrishna
Jonathan NeedlemanOn Branching Laws for Representations of GL4(F) to SP4(F)
Advisor: 
Birgit E. Speh
Artem PulemotovGeometric Flows on Manifolds with Boundary
Advisor: 
Leonard Gross
Biao WangFoliations for Quasi-Fuchsian 3-Manifolds
Advisor: 
William Paul Thurston
James WorthingtonAutomata, Representations, and Proofs
Advisor: 
Dexter Kozen
Zhigen ZhaoDecision Approach and Shrinkage Confidence Intervals
Advisor: 
J.T. Gene Hwang

2008

Bryant AdamsRepresenting Processes as Updated Automata and Transducers
Advisor: 
Anil Nerode
Edoardo Carta-Gerardino Update Transducers and Linear Recurrence Equations over Semirings
Advisor: 
Anil Nerode
Noam Horwitz Free Resolutions of Monomial Ideals
Advisor: 
Irena Peeva
Sarah Koch A New Link Between Teichmüller Theory and Complex Dynamics
Advisor: 
John H. Hubbard
Francesco Matucci Algorithms and Classification in Groups of Piecewise-Linear Homeomorphisms
Advisor: 
Martin Kassabov
Mia Minnes Computability and Complexity Properties of Automatic Structures and their Applications
Advisor: 
Anil Nerode
Michael O'ConnorUsing Tree Automata to Investigate Intuitionistic Propositional Logic
Advisor: 
Richard A. Shore
Jay SchweigPoset Convex-Ear Decompositions and Applications to the Flag h-Vector
Advisor: 
Edward Swartz
John Workman End-Point Estimates and Multi-parameter Paraproducts on Higher Dimensional Tori
Advisor: 
Camil Muscalu
Jessica Zuniga Merging of Some Time Homogeneous and Inhomogeneous Markov Chains
Advisor: 
Laurent Saloff-Coste