# Dissertations

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## 2020

**Elliot Cartee**

Thesis: Topics in Optimal Control and Game Theory

Advisor: Alexander Vladimirsky

First Position: L.E. Dickson Instructor, Department of Mathematics, University of Chicago

**Frederik de Keersmaeker**

Thesis: Displaceability in Symplectic Geometry

Advisor: Tara Holm

**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 Mathematics, Cornell University

**Daoji Huang**

Thesis: A Bruhat Atlas on the Wonderful Compactification of PSO(2n)/SO(2n-1) and A Kazhdan-Lusztig Atlas on G/P

Advisor: Allen Knutson

**Pak-Hin Li**

Thesis: A Hopf Algebra from Preprojective Modules

Advisor: Allen Knutson

**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 Mathematics, University of Illinois at Urbana-Champaign

**Shihao Xiong**

Thesis: Forcing Axioms For Sigma-Closed Posets And Their Consequences

Advisor: Justin Moore

## 2019

**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

**Jun Le Goh**

Thesis: Measuring the Relative Complexity of Mathematical Constructions and Theorems

Advisor: Richard Shore

**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 Mathematics, 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

## 2018

**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 Mathematics, Harvard University

## 2017

**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

## 2016

**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 Mathematics

## 2015

**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

**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

## 2014

**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

## 2013

**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 at the 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

## 2012

**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

## 2011

**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 Mathematics

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

## 2010

**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

## 2009

**Joshua Bowman**

Thesis: Flat Structures and Complex Structures in Teichmüller Theory

Advisor: John H. Hubbard

First position: Lecturer at Stony Brook University

**Nikolai Dimitrov**

Rapid Evolution of Complex Limit Cycles

Advisor: Yulij Ilyashenko

First position: Postdoctoral fellow at McGill University and Centre de Recherches Mathématiques

**Alimjon Eshmatov**

Thesis: Group-Valued Implosion and Conjugation Spaces

Advisor: Reyer Sjamaar

**Bradley Forrest**

Thesis: Degree Subcomplexes of Auter Space and Ribbon Graph Complexes

Advisor: Karen Vogtmann

First position: Assistant professor at the Richard Stockton College of New Jersey

**Chris Lipa**

Thesis: Monodromy and Hénon Mappings

Advisor: John H. Hubbard

First position: postdoc at Göttingen University

**Radu Murgescu**

Thesis: On the p-Class Groups of the Pure Number Field Q(N1/p) and its Galois Closure Q(N1/p, ζp)

Advisor: Ravi Ramakrishna

**Jonathan Needleman**

Thesis: On Branching Laws for Representations of GL4(F) to SP4(F)

Advisor: Birgit E. Speh

First Position: Assistant professor at Oberlin College

**Artem Pulemotov**

Thesis: Geometric Flows on Manifolds with Boundary

Advisor: Leonard Gross

First Position: L.E. Dickson Instructor at the University of Chicago

**Biao Wang**

Thesis: Foliations for Quasi-Fuchsian 3-Manifolds

Advisor: William Paul Thurston

First Position: Visiting assistant professor at University of Toledo (Ohio State)

**James Worthington**

Thesis: Automata, Representations, and Proofs

Advisor: Dexter Kozen

First Position: Visiting lecturer at Cornell University

**Zhigen Zhao**

Thesis: Decision Approach and Shrinkage Confidence Intervals

Advisor: J.T. Gene Hwang

First Position: tenure-track assistant professor of statistics at Temple University's Fox School of Business