2026
- Anish Chedalavada (D. Gepner)
Towards a derived geometry for 2-rings with applications to the representation theory of finite groups - Akira Tominaga (D. Gepner)
On topological Jacobi forms - Yantao Wu (M. Maggioni, Y. Sire)
Low-Dimensional Structure in Nonlinear PDEs and High-Dimensional Statistical Learning - Luqiao Xu (K. Consani)
On the geometry of the absolute point
2025
- Anthony Agwu (E. Riehl)
A Model of Type Theory in Groupoid Assemblies - Xuantao Chen (H. Lindblad)
Asymptotics and Scattering for Relativistic Field Equations - Aditya Kumar (Y. Sire)
Three Problems in Geometric Analysis - Chen-Wei (Milton) Lin (D. Gepner)
The Casselman-Shalika formula in Perfect Geometry - Chutian Ma (B. Dodson)
Global Well-posedness and Scattering of the Schrödinger and Wave equations on Hyperbolic Spaces - Elham Matinpour (J. Bernstein)
Characterization and Morse Index of Minimal Surfaces with Y-singularities - Tomas Mejia Gomez (N. Kitchloo)
Link Homologies, Bott-Samelson Spaces and Twisted Cohomology - Shenrong Wang (D. Savitt)
Moduli of potentially semistable representations - Yanfei Wang (C. Sogge)
Weyl formula improvement on product of Zoll manifolds
2024
- Yang He (V. Shokurov)
Syzygies of Mori fibre spaces - Naurki Masuda (D. Gepner)
The Algebra of Categorical Spectra - Sean Owen (K. Consani)
On Absolute Riemann-Roch and Rings of mu-Polynomials - Jiayi (Nikki) Wang (Y. Sire)
Fujita-type result and self-similar blow-up behavior in a semilinear heat equation with degenerate coefficients - Junfu Yao (J. Bernstein)
On a Mountain-pass Theorem in Hyperbolic Space and its Application
Older Theses
2023
- Qingci An (F. Lu)
Identifiability and data-adaptive RKHS Tikhonov regularization in nonparametric learning problems - Letian Chen (J. Bernstein)
On Mean Curvature Flows coming out of Cones - Ben Dees (C. Mese)
On the Singular Sets of Harmonic Maps into F-Connected Complexes - Lili He (H. Lindblad)
The linear stability of weakly charged and slowly rotating Kerr Newman family of charged black holes - Kalyani Kansal (D. Savitt)
Codimension one intersections between components of the Emerton-Gee stack for GL2 - Quanjun Lang (F. Lu)
Learning kernels with nonlocal dependence in mean-field equations and the extension problem on Dirichlet space - Yujie Luo (Y. Sire)
Minimal log discrepancy and its applications in birational geometry - Keaton Stubis (D. Savitt)
Eisenstein Series with Class Number Coefficients Constructed from the Weil Representation - Rong Tang (Y. Sire)
Nonlocal Filtration Equations and Fractional Curvature Flows - Xiangze Zeng (V. Shokurov)
Boundedness of n-Complements on Algebraic Surfaces - Zehong Zhang (F. Lu)
Multi-agent systems: observability, classification and clustering prediction - Luochen Zhao (Y. Sakellaridis)
Topics in p-adic analysis
2022
- Tslil Clingman (E. Riehl)
Towards a theory of proof relevant categories - Zongyipoan Lin (D. Savitt)
Crystalline lifts of Galois representations - David Myers (E. Riehl)
Symmetry, Geometry, Modality - Caroline VanBlargan (Y. Wang)
Stability of Quermassintegral Inequalities - Junyan Zhang (H. Lindblad)
The Free-Boundary Problems in Inviscid Magnetohydrodynamics with or without Surface Tension - Jin Zhou (M. Maggioni)
Learning multiscale approximations of functions between manifolds
2021
- Daniel Fuentes-Keuthan (E. Riehl)
Goodwillie Towers of Infinity Categories and Desuspension - Xiaoqi Huang (C. Sogge)
Weyl formulae for Schrödinger operators with critically singular potentials - Hanveen Koh (B. Smithling)
Towards a conjecture of Pappas and Rapoport on a scheme attached to the symplectic group - Patrick Martin (M. Maggioni)
Multiplicatively Perturbed Least Squares for Dimension Reduction - Xiyuan Wang (D. Savitt)
Topics in Galois representations
2020
- Jordan Paschke (C. Sogge)
Uniform Weyl Asymptotics for Off-Diagonal Spectral Projections
2019
- Daniel Ginsberg (H. Lindblad)
The free boundary problem for Euler’s equations - Apurva Nakade (N. Kitchloo)
Manifold Calculus and Convex Integration - Cheng Zhang (C. Sogge)
Oscillatory Integrals and Eigenfunction Restriction Estimates - Zehua Zhao (B. Dodson)
Long time dynamics for nonlinear Schrödinger equations at critical regularity
2018
- Christopher Kauffman (H. Lindblad)
Global Stability for Charged Scalar Fields in Spacetimes close to Minkowski - Harry Lang (M. Maggioni)
Streaming Coresets for High-Dimensional Geometry - Tianyi Ren (C. Sogge)
Resolvent Estimates for the Laplacian in the Euclidean Space and on the Sphere - Shengwen Wang (J. Bernstein)
Some results on the entropy of closed hypersurfaces and topology through singularities in mean curvature flow - Emmett Wyman (C. Sogge)
Explicit bounds on integrals of eigenfunctions over curves in surfaces of nonpositive curvature
2017
- Ben Diamond (C. Consani)
Smooth Surfaces in Smooth Fourfolds with Vanishing First Chern Class - Chenyun Luo (H. Lindblad)
On the motion of the free surface of a compressible liquid - Yakun Xi (C. Sogge)
Kakeya-Nikondym Problems and Geodesic Restriction Estimates for Eigenfunctions.
2016
- Jon Beardsley (J. Morava)
Coalgebraic Structure and Intermediate Hopf-Galois Extensions of Thom Spectra in Quasicategories - Stephen Cattell (N. Kitchloo)
The Completion of Dominant K-Theory - Po-Yao Chang (J. Spruck)
Self-shrinkers to the mean curvature flow asymptotic to isoparametric cones - Vitaly Lorman (N. Kitchloo)
Real Johnson-Wilson Theories and Computations - Kalina Mincheva (C. Consani)
Semiring Congruences and Tropical Geometry - Chenyang Su (J. Spruck)
Starshaped locally convex hypersurfaces with curvature and boundary
2015
- Jai Ung Jun (C. Consani)
Algebraic geometry over semi-structure and hyper-structure of characteristic one - John Ross (W. Minicozzi)
Rigidity Results of Lambda-Hypersurfaces - Jeffrey Tolliver (C. Consani)
Hyperstructures and Idempotent Semistructures - Xing Wang (C. Sogge)
Asymptotic Behavior of Spectrums for Elliptic Pesdodifferential Operators - Min Xue (C. Sogge)
Concerning the Klein-Gordon equation on asymptotically Euclidean manifolds - Junyan Zhu (B. Shiffman)
Hole Probabilities of SU(m+1) Gaussian Random Polynomials
2014
- Arash Karami (B. Shiffman)
Zeros of random Reinhardt polynomials - Matthew McGonagle (W. Minicozzi)
The Gaussian Isoperimetric Problem and the Self-Shrinkers of Mean Curvature Flow - Duncan Sinclair (C. Mese)
Heat Kernels on Riemannian Polyhedra and Heat Flows into NPC Manifolds - Hongtan Sun (C. Sogge)
Strichartz Estimates for Wave and Schrödinger Equations on Hyperbolic Trapped Domains - Tim Tran (B. Shiffman)
Continuity of the Asymptotics of Expected Zeros of Fewnomials
2013
- Xuehua Chen (C. Sogge)
An Improvement on eigenfunction restriction estimates for compact boundaryless Riemannian manifolds with nonpositive sectional curvature - Leili Shahriyari (W. Minicozzi)
Translating graphs by mean curvature flow - Peng Shao (C. Sogge)
Sobolev resolvent estimates for the Laplace-Beltrami operator on compact manifolds - Ling Xiao (J. Spruck)
Flow Problems in Hyperbolic Space
2012
- Sinan Ariturk (C. Sogge)
Concentration and vanishing of eigenfunctions on a manifold with boundary - Caleb Hussey (W. Minicozzi)
Classification and analysis of low index mean curvature flow self-shrinkers - Jingzhou Sun (B. Shiffman)
Expected Euler characteristic of excursion sets of random holomorphic sections on complex manifolds
2011
- Joseph Cutrone (V. Shokurov)
Symmetric Sarkisov Links of Fano Threefolds - Michael Limarzi (T. Ono)
On a Cohomological Study of Heisenberg Groups over The Ring of Algebraic Integers - Longzhi Lin (W. Minicozzi)
On the existence of closed geodesics and uniqueness of weakly harmonic maps - Nicholas Marshburn (V. Shokurov)
Smooth Weak Fano Threefolds - Xin Yu (C. Sogge)
Strichartz Estimates and Strauss Conjecture on Various Settings
2010
- John Baber (B. Shiffman)
Scaled correlations of critical points of random sections on Riemann surfaces - Romie Banerjee (J. Boardman, S. Wilson)
Real Johnson-Wilson theories and non-immersions of projective spaces - Jonathan Dahl (C. Mese)
Existence and structure of solutions of Steiner problems in optimal transport - Stephen Kleene (W. Minicozzi)
Singular behavior of minimal surfaces and mean curvature flow
2009
- Susama Agarwala (J. Morava)
The geometry of renormalization - Abhishek Banerjee (C. Consani)
Nearby cycles, Archimedean complex and periodicity in cyclic homology - Christine Breiner (W. Minicozzi)
Embedded minimal surfaces of finite topology and one end - Yifei Chen (V. Shokurov)
Strong rational connectedness of toric varieties - Jing-Cheng Jiang (C. Sogge)
Bilinear Strichartz estimates in two dimensional compact manifolds and cubic nonlinear Schrödinger equations - Hamid Hezari (S. Zelditch)
Eigenvalues and eigenfunctions of Schrödinger operators:
Inverse spectral theory; and the zeros of eigenfunctions - Siddique Khan (W. Minicozzi)
Embedded minimal disks with curvature blow-up on a line segment - Joel Kramer (W. Minicozzi)
Embedded minimal spheres in 3-manifolds - Reza Seyyedali (R. Wentworth)
Balanced metrics in Kahler geometry - Thomas Wright (T. Ono)
On convergence of singular series for a pair of quadratic Forms - Patrick Zulkowski (C. Mese)
The Plateau problem in Alexandrov spaces satisfying the Perel’man conjecture
2008
- Benjamin Baugher (S. Zelditch)
Statistics of critical points in Kahler geometry and string theory - Sung Rak Choi (V. Shokurov)
The geography of log models and its applications - Brian Macdonald (B. Shiffman)
Statistics of non-real zeros and critical points of systems of real random polynomials in several variables - Shuai Wang (T. Ono)
On a certain triple system, elliptic curves and Gauss theory of quadratic forms - Qi Zhong (S. Zelditch)
Energies of zeros of random sections on Riemann surfaces
2007
2006
- Ann Stewart (C. Sogge)
Existence theorems for some nonlinear hyperbolic equations on a waveguide - Hsin-Hao Su (J. Boardman)
The E (1,2) Cohomolgy of the Eilenberg-Mac Lane Space Lane K(Z,3)
2005
- Giuseppe Tinaglia (W. Minicozzi)
Multi-valued Graphs In Embedded Constant Mean Curvature Disks - Mike Krebs (R. Wentworth)
Toledo Invariants on 2-Orbifolds - Eun-Kyoung Lee (T. Ono)
On Certain Cohomological Invariants of Algebraic Number Fields
2004
- Brian Dean (W. Minicozzi)
Some Results on Stable Compact Embedded Minimal Surfaces in 3-Manifolds - Seok-Min Lee (T. Ono)
On Certain Cohomological Invariants of Quadratic Number Fields - Sirong Zhang (W. Minicozzi)
Curvature Estimates for Constant Mean Curvature Surfaces in Three Manifolds - Xiangjin Xu (C. Sogge)
Eigenfunction Estimates on Compact Manifolds with Boundary and Hörmander Multiplier Theorem
2003
- Byungchul Cha (C. Popescu)
Vanishing of Some Cohomology Groups and Bounds for the Shafarevich-Tate Groups of Elliptic Curves - Jason Metcalfe (C. Sogge)
Global Strichartz Estimates for Solutions of the Wave Equation Exterior to a Convex Obstacle
2002
- Jung-Jo Lee (J. Shalika)
Bounding Ranks of Elliptic Curves
2001
- Jihun Park (V. Shokurov)
Fano Fibrations Over a Discrete Valuation Ring - Ramin Takloo-Bighash (J. Shalika)
The Integral of Novodvorsky and the Local p-adic Factors of the Spinor L-function of the Group - Takeshi Torii (J. Morava)
One Dimensional Formal Group Laws of Height N and N-1 - Alexandru Tupan (V. Kolyvagin)
Congruences for Modular Forms - Hemin Yang (J. Boardman, W. Wilson)
The Hit Problem for w (4) over F2 by Differential Operator Algebra
2000
- Ivan Cheltsov (V. Shokurov)
Log Models of Birationally Rigid Varieties - Joshua Neuheisel (S. Zelditch)
The Asymptotic Distribution of Nodal Sets on Spheres - Diego Socolinsky (J. Spruck)
A Variational Approach to Image Fusion
1999
- Terutake Abe (V. Shokurov)
Classification of Exceptional Surface Complements - Florin Ambro (V. Shokurov)
The Adjunction Conjecture Applications - Satyan Devadoss (J. Morava)
Tessellations of Moduli Spaces and the Mosaic Operad - Heuisu Ryu (V. Kolyvagin)
Algorithm for Non-Triviality of Shafarevich-Tate Group Using Heegner Points for Some Family of Elliptic Curves - Guoling Tong (J. Shalika)
The Shimura Integral and the Standard L-function of U(3)