PhD Alumni
Name  Dissertation Title  Faculty Advisor  First Position After Graduating 

Erik Bates 
Localization and free energy asymptotics in disordered statistical mechanics and random growth models  NSF Postdoctoral Fellow, Department of Mathematics, UC Berkeley  
Cédric De Groote 
On the orderability up to conjugation of certain open contact manifolds  Postdoctoral researcher, Max Planck Institute for Mathematics in the Sciences  
Benjamin Fayyazuddin Ljungberg 
Moduli spaces of bundles via motivic probabilities  Member Of Technical Staff at Pickle Robot Co.  
Tony Feng 
Etale Steenrod Operations and the Artin Tate Pairing 
Akshay Venkatesh (Institute for Advanced Study)

CLE Moore Instructor, Department of Mathematics, MIT 
Sarah Peluse 
Bounds for sets with no nontrivial polynomial progressions  NSF Postdoc, Oxford University, then Veblen Instructor at Princeton University and the Institute for Advanced Study  
Chandrasekhar Raju 
Circle method and the Subconvexity problem  Postdoc, Department of Mathematics, École polytechnique fédérale de Lausanne  
Jens Reinhold 
On manifold bundles over classifying spaces 
Ralph Cohen
Soren Galatius (University of Copenhagen)

Postdoctoral researcher, Department of Mathematics, University of Münster 
Jesse Silliman 
On the Arithmetic of Weight Two Eisenstein Series 
Akshay Venkatesh (Institute for Advanced Study)

Research Assistant Professor, Department of Mathematics, Duke University 
Caitlin Stanton 
Chow Groups and Characteristic Numbers on the Space of Complete Quadrics  Software Engineer at Google  
Weston Ungemach 
Deformations of Generalized Fuchsian Representations  Researcher in Applied Machine Learning at Google  
Fan Wei 
On Applications of Szemer\'edi's Regularity Lemma  Postdoctoral position at the Institute for Advanced Study 
Name  Dissertation Title  Faculty Advisor  First Position After Graduating 

Daniel AlvarezGavela 
The flexibility of caustics  Member, Institute for Advanced Study  
Benjamin Dozier 
Saddle connections on translation surfaces 
Steven Kerckhoff
Alex Wright (University of Michigan)

Postdoc at the Fields Institute, then Postdoc at Stony Brook 
Inbar Klang 
Factorization theory of Thom spectra, twists, and duality  Postdoc at EPFL in Switzerland, then Postdoc at Columbia University  
Chao Li 
Singularity and comparison theorems for metrics with positive scalar curvature  Postdoctoral position at Princeton University  
Jesse Madnick 
Nearly Kahler 6 Manifolds of Cohomogeneity Two: Local Theory  Postdoctoral position at McMaster University  
Zev Rosengarten 
Tate Duality in Positive Dimension and Applications  Postdoctoral Fellow at Hebrew University  
Michail Savvas 
Generalized Donaldson Thomas Invariants via Kirwan Blowups  Postdoctoral position at University of California San Diego  
David Sherman 
Schur indices and the p adic Langlands program  Postdoctoral position at the University of Minnesota in Minneapolis  
Gergely Szucs 
The Equivariant Cobordism Category 
Soren Galatius (University of Copenhagen)

Software engineer at Google 
Alex Zhai 
Asymptotics of Gaussian processes and Markov chains  
Yang Zhou 
Higher genus wall crossing in Landau Ginzburg theory  Postdoctoral position at the Center of Mathematical Sciences and Applications at Harvard University 
Name  Dissertation Title  Faculty Advisor  First Position After Graduating 

Zarathustra Brady 
Sieves and Iteration Rules  Instructor in Pure Mathematics/NSF Fellow, MIT  
Daren (Da Rong) Cheng 
Geometric Variational Problems: Regular and Singular Behavior  L. E. Dickson Instructor, University of Chicago  
Alexandra Florea 
Moments and zeros of Lfunctions over function fields  NSF Postdoctoral Fellow, University of Bristol  
Jun Gao 
The front asymptotics for the nonlocal KPP equation  Market Quantitative Associate, Citigroup  
François Greer 
Modular Forms in Enumerative Geometry  Research Assistant Professor, Simons Center for Geometry and Physics, Stony Brook University  
Jafar Jafarov 
Loop Equations and String Dualities in Lattice Gauge Theories  Market Associate, Barclays  
Brian Lawrence 
Two Results on Period Maps  NSF Postdoctoral Research Fellow, Columbia University  
Oleg Lazarev 
Flexible Weinstein structures and applications to symplectic and contact topology  NSF Postdoctoral Research Fellow, Columbia University  
Shotaro Makisumi 
Modular Koszul duality for Soergel bimodules 
Zhiwei Yun

Joseph F. Ritt Assistant Professor, Columbia University 
Christos Mantoulidis 
Geometric Variational Problems in Mathematical Physics  C L E Moore Instructor, MIT  
David Montague 
Covariance Estimation and Graphical Models for Infinite Collections of Random Variables 
Balakanapathy Rajaratnam

Member of the Technical Staff, Palantir Technologies 
Donghai Pan 
Pencils of Fermat hypersurfaces and Galois cyclic covers of the projective line  
Niccolò Ronchetti 
On the mod p derived Hecke algebra of a padic group  Hedrick Assistant Adjunct Professor, UCLA  
Beniada Shabani 
Propagation in multidimensional FisherKPP equations  Postdotoral Fellow, EHESS  
Sverrir Thorvaldsson 
Boundary Fibration Structures and QuasiHomogeneous Geometries  Chief Risk Officer, Islandsbanki  
Evan Warner 
Adic Moduli Spaces  Joseph F. Ritt Assistant Professor, Columbia University  
Graham White 
Combinatorial methods in Markov chain mixing  Zorn Postdoctoral Fellow, Indiana University 
Name  Dissertation Title  Faculty Advisor  First Position After Graduating 

Jeremy Booher 
Geometric Deformations of Orthogonal and Symplectic Galois Representations  Postdoctoral Research Associate, University of Arizona  
Iurie Boreico 
Statistics of random integral matrices  
Valentin Buciumas 
Quantum groups and the YangBaxter equation  
Peter Diao 
Differential Calculus on Graphon Space and Statistical Applications of Graph Limit Theory  Balakanapathy Rajaratnam  
Nicholas Edelen 
On the freeboundary mean curvature flow 
Brian White
Simon Brendle


Daniel Jerison 
The Drift and Minorization Method for Reversible Markov Chains  
Sander Kupers 
Some finiteness results for groups of automorphisms of manifolds  
Evita Nestoridi 
Rates of convergence of Markov chains to stationarity: strong stationary times, coupling, Gelfand pairs and comparison theory.  
Samuel Nolen 
The string topology of holomorphic curves in BU(n).  
David (Weiluo) Ren 
Two models on limit order trading  
Kyler Siegel 
New constructions and computations in rigid and flexible symplectic geometry and applications to several complex variables  
Soarer (Ho Chung) Siu 
Value distribution of Automorphic Forms in a Family  
Jacek Skryzalin 
Numeric Invariants from Multidimensional Persistence  
Arnav Tripathy 
The symmetric power and etale realization functors commute  
Licheng Tsai 
Weak Universality of Interacting Particle Systems  
Sara Kalisnik Verovsek 
Tropical Coordinates on the Space of Persistence Barcodes  
Alexandr Zamorzaev 
GopakumarVafa conjecture for genus 0 real GromovWitten invariants 
Name  Dissertation Title  Faculty Advisor  First Position After Graduating 

Saran Ahuja 
Mean field games with common noise  
Megan Bernstein 
Random Walks on the Symmetric Group, Likelihood Orders, and Involutions  
Otis Chodosh 
The geometry of asymptotically hyperbolic manifolds  
Ralph Furmaniak 
On the Structure and Complex Analysis of Dirichlet Series  
Elizabeth Goodman 
Lagrangian Tori in R^4 and S^2xS^2  
Christopher Henderson 
Propagation Phenomena in ReactionAdvectionDiffusion Equations  
Peter Hintz 
Global analysis of linear and nonlinear wave equations on cosmological spacetimes  
Vitaly Katsnelson 
Diffraction of Elastic Waves by Edges  
Seung Ki Kim 
On the Shape of a HighDimensional Random Lattice  
Jeremy Leach 
The Vacuum Einstein Constraint Equations on Manifolds with Ends of Cylindrical Type  
Daniel Litt 
NonAbelian Lefschetz Hyperplane Theorems  
Sam Nariman 
Stable Moduli of Flat Manifold Bundles  
Khoa Lu Nguyen 
On Symplectic Homology of the Complement of a Positive Normal Crossing Divisor in a Projective Variety  
John Pardon 
A new construction of virtual fundamental cycles in symplectic geometry  
Haizhao Yang 
Oscillatory Data Analysis and Fast Algorithms for Integral Operators 
Name  Dissertation Title  Faculty Advisor  First Position After Graduating 

Ulrik Buchholtz 
Unfolding of Systems of Inductive Definitions  
Alessandro Carlotto 
Rigidity and flexibility phenomena in General Relativity  
Junsoo Ha 
Some problems in multiplicative number theory  
Yuncheng Lin 
On Higher q, tCatalan Numbers  
Cary Malkiewich 
Duality and linear approximations in Hochschild homology, Ktheory, and string topology  
Daniel Kim Murphy 
Algebraic Modular Forms on Definite Orthogonal Groups  
Amy Pang 
Hopf Algebras and Markov Chains  
Jenya Sapir 
Nonsimple geodesics on surfaces  
Fernando (Xuancheng) Shao 
Dichotomy between structure and randomness in combinatorial number theory 
Name  Dissertation Title  Faculty Advisor  First Position After Graduating 

Henry Adams 
Evasion Paths in Mobile Sensor Networks  
Rebecca Bellovin 
padic Hodge theory in rigid analytic families  
Jonathan Campbell 
Some Results on KTheory, Topological Hochschild Homology, and Parameterized Spectra  
Ilya Grigoriev 
Relations Among Characteristic Classes of Manifold Bundles  
Nicholas Haber 
Microlocal analysis of Lagrangian submanifolds of radial points  
Kenji Kozai 
Singular hyperbolic structures on pseudoAnosov mapping tori  
Brandon Levin 
Gvalued flat deformations and local models  
Xiaodong Li 
Sparse and Lowrank Structures in Robust Principal Component Analysis, Compressed Sensing with Corruptions, and Phase Retrieval  
Michael Lipnowski 
Equivariant Torsion and Base Change  
Minyu Peng 
Deviation Inequalities for Eigenvalues of Deformed Random Matrices  
Ian Petrow 
Moments of Automorphic LFunctions and Related Problems  
Nisan Stiennon 
The moduli space of real curves and a Z/2equivariant MadsenWeiss theorem  
James Zhao 
A Random Walk Through Combinatorial Probability  
Xin Zhou 
On the variational methods for minimal submanifolds 
Name  Dissertation Title  Faculty Advisor  First Position After Graduating 

Atoshi Chowdhury 
Compactifying Picard stacks over degenerations of surfaces  
Luís Diogo 
Filtered Floer and symplectic homology via GromovWitten theory  
Sukhada Fadnavis 
Graph Colorings and Graph Limits  
Tsz Ho Fong 
New Results on the Singularity Analysis of the KaehlerRicci Flow  
Kaveh Fouladgar 
Regularity Theory for the Symmetric Minimal Surface Equation  
Robert Hough 
Distribution problems in number theory  
Yunjiang Jiang 
Mixing time of Markov chains on finite and compact Lie groups  
Jonathan Lee 
Stratifications and equivariant cohomology of spaces of uppertriangular squarezero matrices  
Jeremy Miller 
The topology of spaces of JHolomorphic maps to C P^2  
Emmy Murphy 
Loose Legendrian Embeddings in High Dimensional Contact Manifolds  
Tracy Nance 
Equivariant Algebraic KTheory of Products of Motivic Circles  
Ha Pham 
A model diffractive boundary value problem on an asymptotically antide Sitter space  
Simon RubinsteinSalzedo 
Controlling Ramification in Number Fields  
David Sher 
Conic Degeneration and the Determinant of the Laplacian  
Mykhaylo Shkolnikov 
Competing particle systems and their applications  
Aaron Smith 
Some Analyses of Markov Chains by the Coupling Method 
Name  Dissertation Title  Faculty Advisor  First Position After Graduating 

Olena Bormashenko 
Permutations with Interval Restrictions  
Man Chuen Cheng 
A Duality theorem for DeligneMumford Stacks with respect to Morava Ktheory  
Jeffrey Danciger 
Geometric transitions: from hyperbolic to anti de Sitter geometry  
Jesse GellRedman 
On harmonic maps into conic surfaces  
Penka Georgieva 
Orientability of moduli spaces and open GromovWitten invariants  
Jack Hall 
General Existence Theorems in Moduli Theory  
Brian Krummel 
Existence and regularity of branched minimal submanifolds  
Xiannan Li 
The behaviour of Lfunctions at the edge of the critical strip and applications  
Man Chun Li 
On a free boundary problem for embedded minimal surfaces and instability theorems for manifolds with positive isotropic curvature  
Jason Miller 
Limit Theorems for GinzburgLandau Random Surfaces  
Dung Nguyen 
Characteristic numbers of genus one space curves  
Jose Perea 
Topology of Spaces of MicroImages, and an Application to Texture Discrimination  
Anca Vacarescu 
Filtering and Parameter Estimation for Partially Observed Generalized Hawkes Processes 
Name  Dissertation Title  Faculty Advisor  First Position After Graduating 

Dean Baskin 
Wave equations on asymptotically de Sitter spaces  
Yin Chan 
Moduli Spaces of Pseudoholomorphic Disks and Floer Theory of Cleanly Intersecting Immersed  
Vorrapan Chandee 
Upper bounds and moments of Lfunctions  
Dmitriy Ivanov 
Part I: Symplectic ice Part II: Global and local Kubota symbols  
Jennifer Kloke 
Methods and Applications of Topological Data Analysis  
Robin Koytcheff 
A homotopytheoretic view of BottTaubes integrals and knot spaces  
Anssi Lahtinen 
String topology and twisted Ktheory  
Jason (ChiehCheng) Lo 
Moduli Spaces of PTStable Objects  
Eric Malm 
String Topology and the Based Loop Space  
Yujong Tzeng 
A Proof of the GöttscheYauZaslow Formula  
Thomas Williams 
The Motivic Cohomology of Varieties of Long Exact Sequences 
Name  Dissertation Title  Faculty Advisor  First Position After Graduating 

David Ayala 
Geometric Cobordism Categories  
Zachary Cohn 
Nonuniqueness of Constant Scalar Curvature Metrics in a Conformal Class  
Josh Genauer 
Cobordism Categories, Corners, and Surgery  
LanHsuan Huang 
Center of Mass and Constant Mean Curvature Foliations for Isolated Systems  
Daniel Mathews 
Chord Diagrams, ContactTopological Quantum Field Theory, and Contact Categories  
Nikolay Penev 
The Chow ring of the moduli space of genus 6 curves  
Joseph Rabinoff 
HigherLevel Canonical Subgroups for pDivisible Groups  
Eric Schoenfeld 
Higher Symplectic Field Theory Invariants for Cotangent Bundles of Surfaces  
Kamil Szczegot 
Sharp Approximation of Density Dependent Markov Chains  
Kirsten Wickelgren 
Lower Central Series Obstructions to Homotopy Sections of Curves over Number Fields  
Ziyu Zhang 
On Singular Moduli Spaces of Sheaves on K3 Surfaces  
Kaiyuan Zhang 
Two Problems in quantitative Finance 