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PhD Alumni
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 coadvisor: 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 (BioX/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 
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 Ktheory 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  BrillNoether theory over the Hurwitz space  Clay Research Fellow (202227); Junior Fellow, Harvard (202223); Assistant Professor, UC Berkeley 2023  
Panagiotis Lolas  Eigenvalue Shrinkage Methods in HighDimensional Estimation 
Lexing Ying
Iain Johnstone (Statistics)

Quantitative Researcher at Vatic Investments 
Mark Sellke  HighDimensional Problems in Probability, Optimization, and Learning 
Andrea Montanari
Sebastien Bubeck

Member, Institute for Advanced Study (20222023); 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 
Name  Dissertation Title  Faculty Advisor  First Position After Graduating 

Francisco AranaHerrera  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  
FrancoisSimon FauteuxChapleau  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)

CRMISM 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  LongTime 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 
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 
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  
Maksym Radziwill  Zerodistribution and size of the Riemann zetafunction on the critical line.  
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 