**Full text of dissertations can be found on the**

** Stanford University Libraries website**

### 2008-09 ∼ 2007-08 ∼ 2006-07 ∼ 2005-06 ∼ 2004-05

2003-04 ∼ 2002-03 ∼ 2001-02 ∼ 2000-01

### 2008-09

**David Ayala**

Geometric Cobordism Categories

Advisor: **Ralph Cohen**

**Zachary Cohn**

Nonuniqueness of Constant Scalar Curvature Metrics in a Conformal Class

Advisor: **Richard Schoen**

**Josh Genauer**

Cobordism Categories, Corners, and Surgery

Advisor: **Ralph Cohen**

**Lan-Hsuan Huang**

Center of Mass and Constant Mean Curvature Foliations for Isolated Systems

Advisor: **Richard Schoen**

**Daniel Mathews**

Chord Diagrams, Contact-Topological Quantum Field Theory, and Contact Categories

Advisor: **Yakov Eliashberg**

**Nikolay Penev**

The Chow ring of the moduli space of genus 6 curves

Advisor: **Ravi Vakil**

**Joseph Rabinoff**

Higher-Level Canonical Subgroups for p-Divisible Groups

Advisor: **Ravi Vakil**

**Eric Schoenfeld**

Higher Symplectic Field Theory Invariants for Cotangent Bundles of Surfaces

Advisor: **Yakov Eliashberg**

**Kamil Szczegot**

Sharp Approximation of Density Dependent Markov Chains

Advisor: **Amir Dembo**

**Kirsten Wickelgren**

Lower Central Series Obstructions to Homotopy Sections of Curves over Number Fields

Advisor: **Gunnar Carlsson**

**Kaiyuan Zhang**

Two Problems in quantitative Finance

Advisor: **George Papanicolaou**

**Ziyu Zhang**

On Singular Moduli Spaces of Sheaves on K3 Surfaces

Advisor: **Jun Li**

### 2007-08

**Jarod Alper**

Good moduli spaces for Artin stacks

Advisor: **Ravi Vakil**

**Andres Angel**

Cobordism of Orbifolds

Advisor: **Ralph Cohen**

**Theodora Bourni**

C1Alpha Theory for the Prescribed Mean Curvature Equation with Dirichlet Data

Advisor: **Leon Simon**

**Michael Eichmair**

Non-variational existence problems in general relativity

Advisor: **Richard Schoen**

**David Fernandez Duque**

Results in Dynamic Topological Logic

Advisor: **Grigori Mints**

**Isidora Milin**

Orderability of Contactomorphism Groups of Lens Spaces

Advisor: **Yakov Eliashberg**

**Pompiliu Zamfir**

Spherical Spin Glasses

Advisor: **Amir Dembo**

### 2006-07

**Muzaffer Akat**

A Unified Credit Risk Model

Advisor: **George Papanicolaou**

**Kâzim Büyükboduk**

Kolyvagin Systems Over an Iwasawa Algebra

Advisor: **Karl Rubin**

**Huai-Lian Chang**

Donaldson Thomas Invariants of P¹ Scroll

Advisor: **Jun Li**

**Pok Man Cheung**

Supersymmetric Field Theories and Generalized Cohomology

Advisor: **Ralph Cohen**

**Robert Easton**

S3-Covers of Schemes

Advisor: **Ravi Vakil**

**Chad Lawrence Groft**

Isoperimetric Functions on the Universal Covers of Compact Spaces

Advisor: **Richard Schoen**

**Kate Gruher**

String Topology of Classifying Spaces

Advisor: **Ralph Cohen**

**Jian He**

Symplectic Field Theory of Subcritical Stein Manifolds

Advisor: **Yakov Eliashberg**

**Geir Helleloid**

Automorphism Groups of Finite p-Groups: Structure and Applications

Advisor: **Persi Diaconis**

**Peter Kim**

Mathematical Models of the Activation and Regulation of the Immune System

Advisor: **Doron Levy**

**Dana Paquin**

Multiscale Methods for Image Registration

Advisor: **Doron Levy**

**Daniel Ramras**

Stable Representation Theory of Infinite Discrete Groups

Advisor: **Gunnar Carlsson**

**Tiago C. Requeijo**

Modeling Group Dynamics of Phototaxis

Advisor: **Doron Levy**

**Leobardo Rosales**

Minimal Immersions With Prescribed Boundary

Advisor: **Leon Simon**

**Andrew Schultz**

Galois Module Structure of Galois Cohomology

Advisor: **Ravi Vakil**

**Henry Segerman**

Incompressible Surfaces in Hyperbolic Punctured Torus Bundles are Strongly Detected

Advisor: **Steve Kerckhoff**

**Baosen Wu**

A Degeneration Formula of Donaldson-Thomas Invariants

Advisor: **Jun Li**

### 2005-06

**Joseph Blitzstein**

Building Random Objects Sequentially From Characterization to Algorithm

Advisor: **Persi Diaconis**

**Paul-Olivier Dehaye**

Averages over Compact Lie Groups, Twisted by Weyl Characters and Application to Moments of Derivatives of Characteristic Polynomials.

Advisor: **Daniel Bump**

**Daniel Ford**

Probabilities on Cladograms: Introduction to the Alpha Model

Advisors: **Persi Diaconis** and** Susan Holmes**

**Hui-Chuan Huang**

The Resolvent and Scattering Operator on Near-Product-Hyperbolic Spaces

Advisor: **Rafe Mazzeo**

**David Lecomte**

Hidden Functional Equations for Rankin-Selberg Integrals Associated to Real Quadratic Fields

Advisor: **Daniel Bump**

**Robert Lipshitz**

A Heegaard-Floer Invariant of Bordered Three-Manifolds

Advisor: **Yakov Eliashberg**

**Elizabeth Samantha Meckes**

An Infinitesimal Version of Stein’s Method of Exchangeable Pairs

Advisor: **Persi Diaconis**

**Suhas Raghava Nayak**

Equations of Hamilton-Jacobi Type and Their Applications in Finance

Advisor: **George Papanicolaou**

**Yan-Ping Pan**

Endogenous Default, Bond Pricing and Term Structure of Credit Spread Under Stochastic Volatility

Advisor: **George Papanicolaou**

**Julie Marie Rowlett**

Spectral Geometry and Asymptotically Conic Convergence

Advisor: **Rafe Mazzeo**

**Ioannis Sakellaridis**

Unramified Representations of P-Adic Groups on Spherical Varieties

Advisor: **Daniel Bump**

**Alexander Ivanov Sotirov**

Boundary and Interior Convergence for Hard Sphere Mixtures

Advisor: **Tai-Ping Liu**

### 2004-05

**Tarn Adams**

Flat Chains in Banach Spaces

Advisor: **Brian White**

**Pedro Albin**

The Gauss-Bonnet Theorem and Index Theory on Conformally Compact Manifolds

Advisor: **Rafe Mazzeo**

**David Futer**

Angled Triangulations of Link Complements

Advisor: **Steve Kerckhoff**

**Yichi Gu**

Probabilistic Theory for Topological Approximation and Copositive Matrix

Advisor: **Gunnar Carlsson**

**Sanjai Gupta**

Renormalized Seesaw Identities on G L(2,A)

Advisor: **Daniel Bump**

**Byoung-Du Kim**

The PartyConjecture and Algebraic Functional Equations for Elliptic Curves at Primes with Supersingular Reduction

Advisor: **Karl Rubin**

**Dan Lee**

Connected Sums of Special Lagrangian Submanifold

Advisor: **Richard Schoen**

**André da Silva Neves**

Singularities of Lagrangian Mean Curvature Flow

Advisor: **Richard Schoen**

**Brett Parker**

Holomorphic Curves in Lagrangian Torus Fibrations

Advisor: **Yakov Eliashberg**

**José Robredo**

Open-Closed String Topology

Advisor: **Ralph Cohen**

**Mariel Saez Trumper**

Relaxation of the Curve Shortening Flow on the Plane via the Parabolic Ginzburg-Landau Equation

Advisor: **Rafe Mazzeo**

**Danzhu Shi**

Capillary Surfaces at a Re-Entrant Corner

Advisor: **Robert Finn**

### 2003-04

**Dimitrios Cheliotis**

Diffusion in Random Environment and the Renewal Theorem

Advisor: **Amir Dembo**

**Olivier Daviaud**

Brownian Motion, Cauchy Process and the Gaussian Free Field

Advisor: **Amir Dembo**

**Véronique Godin**

A Category of Bordered Fat Graphs and the Mapping Class Group of a Bordered Surface

Advisor: **Ralph Cohen**

**Michel Grueneberg**

The Yamabe Flow on Three-Manifolds

Advisor: **Richard Schoen**

**Eric Edward Katz**

A Formalism for Relative Gromov-Witten Invariants

Advisor: **Yakov Eliashberg**

**Tyler Lawson**

Derived Representation Theory of Nilpotent Groups

Advisor: **Gunnar Carlsson**

**David Linnan Li**

The Green’s Function of the Navier-Stokes Equations for Gas Dynamics in R³

Advisor: **Tai-Ping Liu**

**Jessica Purcell**

Cusp Shapes of Hyperbolic Link Complements and Dehn Filling

Advisor: **Steve Kerckhoff**

**Christopher Ryan Vinroot**

Twisted Frobenius-Schur Indicators of Symplectic Groups Over a Finite Field

Advisor: **Daniel Bump**

**Yu Yan**

Some Geometric Problems Involving Conformal Deformation of Metrics

Advisor: **Richard Schoen**

**Ke Zhu**

Degeneration of the Moduli Space of J-holomorphic Discs and Legendrian Contact Homology

Advisor: **Yakov Eliashberg**

### 2002-03

**Kirsten Jan Boyd**

Methods for the Approximate Computation of Homogenized Coefficients

Advisor: **George Papanicolaou**

**Theodore Hwa**

Galois Representations Associated to Torsion Points of Elliptic Curves

Advisor: **Karl Rubin**

**Alexander Ivrii**

Lagrangian Unnottedness of Tori in Certain Symplectic 4-Manifolds

Advisor: **Yakov Eliashberg**

**Pengzi Miao**

On Variational Problems in Geometry and General Relativity

Advisor: **Richard Schoen**

**Jacob Shapiro**

Counting BPS States of D-Branes in Calabi-Yau Threefolds

Advisor: **Jun Li**

**Scott Sheffield**

Random Surfaces: Large Deviations Principles and Gradient Gibbs Measure Classifications

Advisor: **Amir Dembo**

### 2001-02

**Frédéric Bourgeois**

A Morse-Bott Approach to Contact Homology

Advisor: **Yakov Eliashberg**

**Nikos Frantzikinakis**

The Structure of Non-Ergodic Strongly Stationary Systems

Advisor: **Yitzhak Katznelson**

**Urmi Bhattacharya Holz**

Subspace Approximation Methods for Perturbed Quadratic Eigenvalue Problems

Advisor: **Gene Golub**

**Benjamin Howard**

The Heegner Point Kolyvagin System

Advisor: **Karl Rubin**

**Yevgeniy Kovchegov**

Brownian Bridge Percolation and Related Processes

Advisor: **Amir Dembo**

**Heaseung Kwon**

Asymptotic Convergence of Harmonic Map Heat Flow

Advisor: **Leon Simon**

**Alexander Meadows**

A Semilinear Elliptic Equation

Advisor: **Leon Simon**

**Weiyang Qiu**

Variational Approach in Special Lagrangian Geometry

Advisor: **Richard Schoen**

**Joshua Sabloff**

Invariants of Legendrian Knots in Circle Bundles

Advisor: **Yakov Eliashberg**

**João Monteiro dos Santos**

Topology of Moduli Spaces of Rank Stable Instantons and Holomorphic Bundles

Advisor: **Ralph Cohen**

**Jay-Calvin Uyemura Reyes**

Random Walk, Semi-Direct Products, and Card Shuffling

Advisor: **Persi Diaconis**

**Maria Joana Mendes Ventura**

Homological Algebra for the Representation Green Functor for Abelian Groups

Advisor: **Gunnar Carlsson**

**Neshan Wickramsekera**

Rigidity of Tangent Cones and the Singular Set of Minimal Hypersurfaces

Advisor: **Leon Simon**

### 2000-01

**Peter Cotton**

An Analytic Approach to Ornstein-Uhlenbeck Processes with Fluctuating Parameters and Applications in the Modeling of Fixed Income Securities

Advisor: **George Papanicolaou**

**Seung-Yeal Ha**

L¹ Stability for Systems of Conservation Laws with a Non-Resonant Moving Source

Advisor: **Tai-Ping Liu**

**Sang Seon Kim**

Relative Contact Homology and Contact Non-Squeezing

Advisor: **Yakov Eliashberg**

**Kirill Michatchev**

Invariants of Legendrian and Transversal Links

Advisor: **Yakov Eliashberg**

**Dana Powell Rowland**

Bott-Periodic Phenomena in Holomorphic K-Theory

Advisor: **Ralph Cohen**

**Xin Wei Sha**

Differential Geometric Performance and the Technologies of Writing

Advisor: **Rafe Mazzeo**

**Xiaofeng Sun**

On the Theory of Harmonic Maps to Trees

Advisor: **Richard Schoen**

**Xiaodong Wang**

On the Geometry of Conformally Compact Einstein Manifolds

Advisor: **Richard Schoen**