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PhD Alumni

Graduation Year:
Name Dissertation Title Faculty Advisor First Position After Graduating
Sanchit Chaturvedi Global properties of kinetic plasmas Simons Junior Fellow, Courant institute
Daren Chen Some variations of Khovanov homology for null homologous links in RP^3 Olga Taussky & John Todd Teaching Fellowship, Division of Physics, Mathematics and Astronomy, Caltech
Sean Cotner Centralizers in reductive group schemes Postdoctoral Assistant Professor, University of Michigan
Simona Diaconu Large Powers of Random Matrices Courant instructor Department of Mathematics, NYU
Panagiotis Dimakis A study on the Extended Bogomolny equations Postdoc, Université du Québec à Montréal
Daniel Dore Reciprocity Laws and Identity Based Encryption
Brian Conrad Unofficial co-advisor: Dan Boneh (CS)
Cryptographer, MobileCoin
Paul Falcone A Plurisubharmonic Analogue to Igusa s Theorem Quantitative Analytics Specialist, Wells Fargo
Felipe Hernandez A New Approach to the Diffusive Limit of the Random Schrodinger Equation NSF Postdoc, Mathematics, MIT
Zachary Izzo Theory and Algorithms for Data Centric Machine Learning
Lexing Ying James Zou (Bio-X/EE/CS)
Researcher, Machine Learning, NEC Labs North America
Boon Hou Derek Khu Ihara's lemma and multiplicity one Research Scientist, Institute for Infocomm Research, Singapore
Sophie Libkind Composition and Computation in Dynamical Systems Postdoc, Topos Institute
Yang Liu Sparsification, Online Optimization, and Maximum Flow in Almost Linear Time
Jan Vondrák Aaron Sidford (Management Science and Engineering and Computer Science)
Postdoc, Institute for Advanced Study
Sammy Luo Methods for problems in generalized Ramsey theory NSF Postdoctoral Research Fellow, MIT
Wyatt Mackey A parameterized Adams spectral sequence for topological data Postdoc, University of Tennessee, Knoxville
Slava Naprienko Combinatorics of integrable lattice models Postdoc, University of North Carolina at Chapel Hill
Huy Pham The emergence of structures in random processes and random graphs Clay Research Fellow, Clay Math Institute
Lie Qian Potential Automorphy for General Linear Groups Dickson Instructor, University of Chicago
Libby Taylor Brauer classes, Azumaya algebras, and higher analogues
Graduation Year:
Name Dissertation Title Faculty Advisor First Position After Graduating
Dylan Cant A dimension formula for relative symplectic field theory Postdoc, University of Montreal
Yue Hui Mean field methods for stochastic control and optimization problems
George Papanicolaou Jose Blanchet (Management Science and Engineering), Peter Glynn (Management Science and Engineering)
Facebook in NYC
Naomi Kraushar Equivariant algebraic K-theory of profinite Bieberbach group actions Teaching postdoc, University of Utah Department of Mathematics
Vivian Kuperberg Sums of singular series and the distribution of primes NSF Postdoc, Department of Mathematics, Tel Aviv University
Hannah Kerner Larson Brill--Noether theory over the Hurwitz space Clay Research Fellow (2022-27); Junior Fellow, Harvard (2022-23); Assistant Professor, UC Berkeley 2023
Panagiotis Lolas Eigenvalue Shrinkage Methods in High-Dimensional Estimation
Lexing Ying Iain Johnstone (Statistics)
Quantitative Researcher at Vatic Investments
Mark Sellke High-Dimensional Problems in Probability, Optimization, and Learning
Andrea Montanari Sebastien Bubeck
Member, Institute for Advanced Study (2022-2023); Assistant Professor, Harvard Statistics (starting Fall 2023)
Mackenzie Simper Double Coset Markov Chains Postdoc, Broad Institute
Yuval Wigderson New constructions in Ramsey theory Postdoc at Tel Aviv University
Kevin Yang Universality for some Random Growth Models NSF postdoc, UC Berkeley; NSF Postdoc & Benjamin Peirce Fellow, Harvard
Graduation Year:
Name Dissertation Title Faculty Advisor First Position After Graduating
Francisco Arana-Herrera Effective mapping class group dynamics Member, Institute for Advanced Study + Brin Postdoctoral Fellow, University of Maryland
Calista Bernard Twisted homology operations
Soren Galatius (University of Copenhagen)
University of Minnesota, Dunham Jackson Assistant Professor (Department of Mathematics)
Ipsita Datta LAGRANGIAN COBORDISMS BETWEEN ENRICHED KNOT DIAGRAMS Postdoc Member, Institute for Advanced Study, Princeton
Sheela Devadas Morphisms and cohomological comparison for Henselian schemes NSF Mathematical Sciences Postdoctoral Research Fellowship, University of Washington Department of Mathematics
Francois-Simon Fauteux-Chapleau Invariants of codimension 2 contact submanifolds
Cole Graham Long time asymptotics for reaction diffusion and stochastic Burgers equations Prager Assistant Professor of Applied Mathematics, Brown University
Jorge Guijarro Ordonez Stochastic control and deep learning approaches to high dimensional statistical arbitrage
Jimmy He Probability on groups: Random walks and limit theorems CLE Moore Instructor, Department of Mathematics, MIT
Xiaoyu He The probabilistic method in combinatorics NSF Postdoc, Mathematics Department, Princeton University
Joseph Helfer Holomorphic curve invariants of open contact manifolds Assistant Professor, Mathematics, University of Southern California
Nick Kuhn Gauge Theoretic Invariants in Algebraic Geometry Max Planck Institute, Guest Researcher
Aaron Landesman A thesis of minimal degree: two NSF Postdoctoral Research Fellow at Harvard University
Jonathan Love Isogeny Graphs, Zero Cycles, and Modular Forms: Computations over Algebraic Curves and Surfaces
Ravi Vakil Akshay Venkatesh (IAS), Dan Boneh (Stanford CS Department)
CRM-ISM Postdoctoral Fellow at the Centre de recherches mathématiques
Sarah McConnell Degree One Contributions and Open Gromov Witten Invariants
Dat Nguyen On hyperbolic cone metrics, PSL 2,R character varieties, and branched coverings
Andrea Ottolini Birthday problems and rates of convergence for Gibbs sampling Postdoctoral Scholar at University of Washington, Seattle
Mark Perlman Dark Pool Trading: Stochastic Control Meets Adaptive Allocation Quantitative Researcher at Optiver
Arpon Raksit The Filtered Circle
Brian Conrad Soren Galatius (University of Copenhagen)
NSF Postdoctoral Fellow, Department of Mathematics, MIT
Leila Sloman Long-Time Behavior of the International Trade Equation
Ka Yu Tam Tamagawa numbers of smooth connected groups
Bogdan Zavyalov Mod p Poincare Duality in p adic Analytic Geometry 1 year postdoc at MPIM, then 3 year postdoc at UM
Zhengqing Zhou Distributionally Robust Optimization and its Applications in Mathematical Finance, Statistics, and Reinforcement Learning
George Papanicolaou Jose Blanchet (Management Science and Engineering), Peter Glynn (Management Science and Engineering)
Quantitative Researcher, Susquehanna International Group
Joey (Yuzhou) Zou Microlocal analysis with applications to seismic inverse problems Postdoc, Department of Mathematics, University of California, Santa Cruz
Graduation Year:
Name Dissertation Title Faculty Advisor First Position After Graduating
Laurent Cote On Linking of Lagrangians in Symplectic 4 Manifolds
Gurbir Dhillon Geometric representations of W algebras and applications to the quantum Langlands correspondence
Daniel Bump Zhiwei Yun (MIT)
Alexander Dunlap Asymptotic properties of some random evolutions and geometries
Ben (David) Lim Algebraization theorems for coherent sheaves on stacks
Ravi Vakil Jarod Alper (University of Washington)
Qingyun Sun Optimization based Modeling in Investment and Data Science
David Donoho (Statistics), Stephen Boyd (Electrical Engineering)
Katerina Velcheva MEAN FIELD MODEL FOR KNOWLEDGE PROPAGATION AND ECONOMIC GROWTH
Guanyang Wang Topics in Markov Chain Monte Carlo Methods, with Applications in Statistics
Abigail Ward Homological mirror symmetry for elliptic Hopf surfaces
Adva Wolf Convex Projective Geometrically Finite Structures
Evangelie Zachos The X Ray Transform on Asymptotically Euclidean Spaces
Scott (Sicong) Zhang Morse Bott Contact Homology via Virtual Fundamental Cycles
Jupiter (Beite) Zhu Radial estimate of isotropic pseudo differential operators via FBI transform
Graduation Year:
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
Graduation Year:
Name Dissertation Title Faculty Advisor First Position After Graduating
Daniel Alvarez-Gavela 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
Graduation Year:
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 L-functions over function fields NSF Postdoctoral Fellow, University of Bristol
Jun Gao The front asymptotics for the non-local 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 p-adic group
Hedrick Assistant Adjunct Professor, UCLA
Beniada Shabani Propagation in multi-dimensional Fisher-KPP equations Postdotoral Fellow, EHESS
Sverrir Thorvaldsson Boundary Fibration Structures and Quasi-Homogeneous 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
Graduation Year:
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 Yang-Baxter equation
Peter Diao Differential Calculus on Graphon Space and Statistical Applications of Graph Limit Theory
Balakanapathy Rajaratnam
Nicholas Edelen On the free-boundary 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
Li-cheng Tsai Weak Universality of Interacting Particle Systems
Sara Kalisnik Verovsek Tropical Coordinates on the Space of Persistence Barcodes
Alexandr Zamorzaev Gopakumar-Vafa conjecture for genus 0 real Gromov-Witten invariants
Graduation Year:
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 Reaction-Advection-Diffusion 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 High-Dimensional Random Lattice
Jeremy Leach The Vacuum Einstein Constraint Equations on Manifolds with Ends of Cylindrical Type
Daniel Litt Non-Abelian 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
Graduation Year:
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, t-Catalan Numbers
Cary Malkiewich Duality and linear approximations in Hochschild homology, K-theory, and string topology
Daniel Kim Murphy Algebraic Modular Forms on Definite Orthogonal Groups
Amy Pang Hopf Algebras and Markov Chains
Jenya Sapir Non-simple geodesics on surfaces
Fernando (Xuancheng) Shao Dichotomy between structure and randomness in combinatorial number theory
Graduation Year:
Name Dissertation Title Faculty Advisor First Position After Graduating
Henry Adams Evasion Paths in Mobile Sensor Networks
Rebecca Bellovin p-adic Hodge theory in rigid analytic families
Jonathan Campbell Some Results on K-Theory, 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 pseudo-Anosov mapping tori
Brandon Levin G-valued flat deformations and local models
Xiaodong Li Sparse and Low-rank 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 L-Functions and Related Problems
Maksym Radziwill Zero-distribution and size of the Riemann zeta-function on the critical line.
Nisan Stiennon The moduli space of real curves and a Z/2-equivariant Madsen-Weiss theorem
James Zhao A Random Walk Through Combinatorial Probability
Xin Zhou On the variational methods for minimal submanifolds
Graduation Year:
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 Gromov-Witten theory
Sukhada Fadnavis Graph Colorings and Graph Limits
Tsz Ho Fong New Results on the Singularity Analysis of the Kaehler-Ricci 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 upper-triangular square-zero matrices
Jeremy Miller The topology of spaces of J-Holomorphic maps to C P^2
Emmy Murphy Loose Legendrian Embeddings in High Dimensional Contact Manifolds
Tracy Nance Equivariant Algebraic K-Theory of Products of Motivic Circles
Ha Pham A model diffractive boundary value problem on an asymptotically anti-de Sitter space
Simon Rubinstein-Salzedo 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
Graduation Year:
Name Dissertation Title Faculty Advisor First Position After Graduating
Olena Bormashenko Permutations with Interval Restrictions
Man Chuen Cheng A Duality theorem for Deligne-Mumford Stacks with respect to Morava K-theory
Jeffrey Danciger Geometric transitions: from hyperbolic to anti de Sitter geometry
Jesse Gell-Redman On harmonic maps into conic surfaces
Penka Georgieva Orientability of moduli spaces and open Gromov-Witten invariants
Jack Hall General Existence Theorems in Moduli Theory
Brian Krummel Existence and regularity of branched minimal submanifolds
Xiannan Li The behaviour of L-functions 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 Ginzburg-Landau Random Surfaces
Dung Nguyen Characteristic numbers of genus one space curves
Jose Perea Topology of Spaces of Micro-Images, and an Application to Texture Discrimination
Anca Vacarescu Filtering and Parameter Estimation for Partially Observed Generalized Hawkes Processes
Graduation Year:
Name Dissertation Title Faculty Advisor First Position After Graduating
Dean Baskin Wave equations on asymptotically de Sitter spaces
Yin Chan Moduli Spaces of Pseudo-holomorphic Disks and Floer Theory of Cleanly Intersecting Immersed
Vorrapan Chandee Upper bounds and moments of L-functions
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 homotopy-theoretic view of Bott-Taubes integrals and knot spaces
Anssi Lahtinen String topology and twisted K-theory
Jason (Chieh-Cheng) Lo Moduli Spaces of PT-Stable Objects
Eric Malm String Topology and the Based Loop Space
Yu-jong Tzeng A Proof of the Göttsche-Yau-Zaslow Formula
Thomas Williams The Motivic Cohomology of Varieties of Long Exact Sequences
Graduation Year:
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
Lan-Hsuan Huang Center of Mass and Constant Mean Curvature Foliations for Isolated Systems
Daniel Mathews Chord Diagrams, Contact-Topological Quantum Field Theory, and Contact Categories
Nikolay Penev The Chow ring of the moduli space of genus 6 curves
Joseph Rabinoff Higher-Level Canonical Subgroups for p-Divisible 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