# Recent PhD Theses

##### 2019

Daniel Ginsberg (Lindblad)

The free boundary problem for Euler’s equations

Apruva Nakade (Kitchloo)

Manifold Calculus and Convex Integration

Cheng Zhang (Sogge)

Oscillatory Integrals and Eigenfunction Restriction Estimates

Zehua Zhao (Dodson)

Long time dynamics for nonlinear Schrödinger equations at critical regularity

##### 2018

Christopher Kauffman (Lindblad)

Global Stability for Charged Scalar Fields in Spacetimes close to Minkowski

Harry Lang (Maggioni)

Streaming Coresets for High-Dimensional Geometry

Tianyi Ren (Sogge)

Resolvent Estimates for the Laplacian in the Euclidean Space and on the Sphere

Shengwen Wang (Bernstein)

Some results on the entropy of closed hypersurfaces and topology through singularities in mean curvature flow

Emmett Wyman (Sogge)

Explicit bounds on integrals of eigenfunctions over curves in surfaces of nonpositive curvature

##### 2017

Ben Diamond (Consani)

Smooth Surfaces in Smooth Fourfolds with Vanishing First Chern Class

Chenyun Luo (Lindblad)

On the motion of the free surface of a compressible liquid

Yakun Xi (Sogge)

Kakeya-Nikondym Problems and Geodesic Restriction Estimates for Eigenfunctions.

##### 2016

Jon Beardsley (Morava)

Hopf-Galois Extensions and Descent Data in Quasicategories

Stephen Cattell (Kitchloo)

The Completion of Dominant K-Theory

Po-Yao Chang (Spruck)

self-shrinkers to the mean curvature flow asymptotic to isoparametric cones

Vitaly Lorman (Kitchloo)

Real Johnson-Wilson Theories and Computations

Kalina Mincheva (Consani)

Semiring Congruences and Tropical Geometry

Chenyang Su (Spruck)

Starshaped locally convex hypersurfaces with curvature and boundary

##### 2015

Jai Ung Jun (Consani)

Algebraic geometry over semi-structure and hyper-structure of characteristic one<

John Ross (Minocozz)

Rigidity Results of Lambda-Hypersurfaces

Jeffrey Tolliver (Consani)

Hyperstructures and Idempotent Semistructures

Xing Wang (Sogge)

Asymptotic Behavior of Spectrums for Elliptic Pesdodifferential Operators

Min Xue (Sogge)

Concerning the Klein-Gordon equation on asymptotically Euclidean manifolds

Junyan Zhu (Shiffman)

Hole Probabilities of SU(m+1) Gaussian Random Polynomials

##### 2014

Arash Karami (B. Shiffman)

Zeros of random Reinhardt polynomials

Matthew McGonagle (W. Minicozz)

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. Minicozz)

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

Scott Zrebiec (B. Shiffman)

Hole Probability and Large Deviations in the Distribution of the Zeros of Gaussian Random Holomorphic Functions

##### 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 (JM Boardman, WS Wilson)

The Hit Problem for w (4) over F_{2} 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)