Recent Ph.D. Recipients

(Click on a student’s name to see his/her dissertation abstract.)

January 2015 (expected)         
Student   Advisor   Dissertation
Yasemin Kara   John H. Hubbard   TBA
Chor Hang Lam   Allen Hatcher   TBA
August 2014        
Student   Advisor   Dissertation
Margarita Amchislavska   Timothy Riley   The geometry of generalized Lamplighter groups
Hyungryul Baik   John H. Hubbard   Laminations on the circle and hyperbolic geometry
Adam Bjorndahl   Anil Nerode and Joseph Halpern   Language-based games
Chi-Kwong Fok   Reyer Sjamaar   The real k-theory of compact Lie groups and almost symplectically isotropic realizations of twisted Poisson manifolds 
Kathryn Lindsey   John Smillie   Families of dynamical systems associated to translation surfaces
Andrew Marshall   Allen Hatcher   On configuration spaces of graphs
Diana Ojeda Aristizabal   Justin Moore   Ramsey theory and the geometry of Banach spaces
Baris Ugurcan   Robert Strichartz   $L^p$-estimates and polyharmonic boundary value problems on the Sierpinski gasket and gaussian free fields on high dimensional Sierpinski carpet graphs
May 2014         
Student   Advisor   Dissertation
Hung Tran   Xiaodong Cao   Aspects of the Ricci flow 
January 2014         
Student   Advisor   Dissertation
Youssef El Fassy Fihry   Yuri Berest   Graded Cherednik Algebra And Quasi-Invariant Differential Forms
Robyn Miller   John Smillie   Symbolic Dynamics Of Billiard Flow In Isosceles Triangles
August 2013        
Student   Advisor   Dissertation
Anna Bertiger   Allen Knutson   The Combinatorics and Geometry of the Orbits of the Symplectic Group on Flags in Complex Affine Space
Mariya Bessonov   Richard Durrett   Probabilistic Models for Population Dynamics
Kristine Jones   Michael Stillman   Generic Initial Ideals of Locally Cohen-Macaulay Space Curves
Remus Radu   John H. Hubbard   Topological models for hyperbolic and semi-parabolic complex Hénon maps
Raluca Tanase   John H. Hubbard   Hénon maps, discrete groups and continuity of Julia sets
Ka Yue (Daniel) Wong   Dan M. Barbasch   Dixmier Algebras on Complex Classical Nilpotent Orbits and their Representation Theories
Tianyi Zheng   Laurent Saloff-Coste   Random walks on some classes of solvable groups
May 2013         
Student   Advisor   Dissertation
Igors Gorbovickis   Yulij Ilyashenko   Some Problems from Complex Dynamical Systems and Combinatorial Geometry
Shisen Luo   Tara Holm   Hard Lefschetz Property of Hamiltonian GKM Manifolds
January 2013        
Student   Advisor   Dissertation
Marisa Hughes   Edward Swartz   Quotients of Spheres by Linear Actions of Abelian Groups
Peter Luthy   Camil Muscalu   Bi-parameter Maximal Multilinear Operators
Jenna Rajchgot   Allen Knutson   Compatibly Split Subvarieties of the Hilbert Scheme of Points in the Plane
August 2012        
Student   Advisor   Dissertation
Juan Alonso   Karen Vogtmann   Graphs of Free Groups and their Measure Equivalence
Jason Anema   Robert Strichartz   Counting Spanning Trees on Fractal Graphs
Janna Lierl   Laurent Saloff-Coste   Heat Kernel Estimates on Inner Uniform Domains
Fatima Mahmood   Reyer Sjamaar   Jacobi Structures and Differential Forms on Contact Quotients
Philipp Meerkamp   John Guckenheimer   Singular Hopf Bifurcation
Milena Pabiniak   Tara Holm   Hamiltonian Torus Actions in Equivariant Cohomology and Symplectic Topology
Peter Samuelson   Yuri Berest   Kauffman Bracket Skein Modules and the Quantum Torus
January 2012        
Student   Advisor   Dissertation
Saúl Blanco Rodríguez   Louis Billera   Shortest Path Poset of Bruhat Intervals and the Complete cd -Index
George Khachatryan   Yuri Berest   Derived Representation Schemes and Non-commutative Geometry
Victor Kostyuk   Karen Vogtmann   Outer Space for Two-Dimensional RAAGs and Fixed Point Sets of Finite Subgroups
August 2011        
Student   Advisor   Dissertation
Owen Baker   Karen Vogtmann   The Jacobian Map on Outer Space
Jennifer Biermann   Irena Peeva   Free Resolutions of Monomial Ideals
Mingzhong Cai   Richard Shore   Elements of Classical Recursion Theory: Degree-Theoretic Properties and Combinatorial Properties
Ri-Xiang Chen   Irena Peeva   Hilbert Functions and Free Resolutions
Denise Dawson   Kenneth Brown   Complete Reducibility in Euclidean Twin Buildings
Paul Shafer   Richard Shore   On the Complexity of Mathematical Problems: Medvedev Degrees and Reverse Mathematics
Russ Thompson   Laurent Saloff-Coste   Random Walks and Subgroup Geometry
Gwyneth Whieldon   Michael Stillman   Betti Numbers of Stanley-Reisner Ideals
May 2011        
Student   Advisor   Dissertation
Mihai Bailesteanu   Xiaodong Cao   The Heat Equation under the Ricci Flow
Samuel Kolins   Edward Swartz   Face Vectors of Subdivision of Balls
Ho Hon Leung   Reyer Sjamaar   K-Theory of Weight Varieties and Divided Difference Operators in Equivariant KK-Theory
Benjamin Lundell   Ravi Ramakrishna   Selmer Groups and Ranks of Hecke Rings
Eyvindur Ari Palsson   Camil Muscalu   Lp Estimates for a Singular Integral Operator Motivated by Calderón’s Second Commutator
Santi Tasena   Laurent Saloff-Coste   Heat Kernel Analysis on Weighted Dirichlet Spaces
January 2011        
Student   Advisor   Dissertation
Michelle Snider   Allen Knutson   Affine Patches on Positroid Varieties and Affine Pipe Dreams
August 2010        
Student   Advisor   Dissertation
Andrew Cameron   Alfred Schatz   Estimates for Solutions of Elliptic Partial Differential Equations with Explicit Constants and Aspects of the Finite Element Method for Second-Order Equations
Timothy Goldberg   Reyer Sjamaar   Hamiltonian Actions in Integral Kähler and Generalized Complex Geometry

Gregory Muller

  Yuri Berest   The Projective Geometry of Differential Operators
Matthew Noonan   John Hubbard    
Sergio Pulido Niño   Philip Protter   Financial Markets with Short Sales Prohibition
August 2009        
Student   Advisor   Dissertation
Joshua Bowman   John Hubbard   Flat Structures and Complex Structures in Teichmüller Theory
Nikolai Dimitrov   Yulij Ilyashenko   Rapid Evolution of Complex Limit Cycles
Alimjon Eshmatov   Reyer Sjamaar   Group-Valued Implosion and Conjugation Spaces
Chris Lipa   John Hubbard   Monodromy and Hénon Mappings
Jonathan Needleman   Birgit Speh   On Branching Laws for Representations of GL4(F) to SP4(F)
Artem Pulemotov   Leonard Gross   Geometric Flows on Manifolds with Boundary
Biao Wang   William Thurston   Foliations for Quasi-Fuchsian 3-Manifolds
James Worthington   Dexter Kozen   Automata, Representations, and Proofs
Zhigen Zhao   J. T. Gene Hwang   Decision Approach and Shrinkage Confidence Intervals
May 2009        
Student   Advisor   Dissertation
Bradley Forrest   Karen Vogtmann   Degree Subcomplexes of Auter Space and Ribbon Graph Complexes
January 2009        
Student   Advisor   Dissertation
Radu Murgescu   Ravi Ramakrishna   On the p-Class Groups of the Pure Number Field Q(N1/p) and its Galois Closure Q(N1/p, ζp)
August 2008        
Student   Advisor   Dissertation
Bryant Adams   Anil Nerode   Representing Processes as Updated Automata and Transducers
Edoardo Carta   Anil Nerode   Update Transducers and Linear Recurrence Equations over Semirings
Noam Horwitz   Irena Peeva   Free Resolutions of Monomial Ideals
Sarah Koch   John Hubbard   A New Link Between Teichmüller Theory and Complex Dynamics
Francesco Matucci   Kenneth Brown and Martin Kassabov   Algorithms and Classification in Groups of Piecewise-Linear Homeomorphisms
Mia Minnes   Anil Nerode   Computability and Complexity Properties of Automatic Structures and their Applications
Michael O'Connor   Richard Shore   Using Tree Automata to Investigate Intuitionistic Propositional Logic
John Workman   Camil Muscalu   End-Point Estimates and Multi-parameter Paraproducts on Higher Dimensional Tori
Jessica Zuniga   Laurent Saloff-Coste   Merging of Some Time Homogeneous and Inhomogeneous Markov Chains
May 2008        
Student   Advisor   Dissertation
Jay Schweig   Edward Swartz   Poset Convex-Ear Decompositions and Applications to the Flag h-Vector
August 2007        
Student   Advisor   Dissertation
Farkhod Eshmatov   Yuri Berest   The Calogero-Moser Correspondence for Noncommutative Deformations of Kleinian Singularities
Pavel Gyrya   Laurent Saloff-Coste   Heat Kernel Estimates for Inner Uniform Subsets of Harnack-Type Dirichlet Spaces
Henri Johnston   Ravi Ramakrishna   The Trace Map and Galois Module Structure of Rings of Integers for Absolutely Abelian Number Fields
Achilleas Sinefakopoulos   Michael Stillman   On Some Classes of Borel Fixed Ideals and their Cellular Resolutions
Mauricio Velasco   Michael Stillman   Monomial Resolutions and the Cox Rings of Del Pezzo Surfaces
May 2007        
Student   Advisor   Dissertation
Jason Bode   Kenneth Brown   Isoperimetric Constants and Self-Avoiding Walks and Polygons on Hyperbolic Coxeter Groups
Benjamin Chan   Richard Durrett   Coexistence of Contact Process
Andrei Maxim   Lars Wahlbin   Aspects of the Finite Element Method for Elliptic Partial Differential Equations
January 2007        
Student   Advisor   Dissertation
Evgueni Klebanov   Laurent Saloff-Coste   Asymptotic Behavior of Convolutions of Centered Density on Lie Group of Polynomial Volume Growth
Vadims Moldavskis   Yulij Ilyashenko   New Generic Properties of Real and Complex Dynamical Systems
Aaron Solo   Lars Wahlbin   Finite Element Methods for Elliptic and Parabolic Problems with Low Regularity Boundary Data
Treven Wall   Leonard Gross   A Fatou Theorem for a Class of Quasi-linear Elliptic Partial Differential Equations
August 2006        
Student   Advisor   Dissertation
Drew Armstrong   Louis Billera   Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups
Kristin Camenga   Louis Billera   Angle Sums on Polytopes and Polytopal Complexes
Guan-Yu Chen   Laurent Saloff-Coste   The Cutoff Phenomenon for Finite Markov Chains
William Gryc   Leonard Gross   On the Holonomy of the Coulomb Connection over 3-Manifolds with Boundary
Jason Martin   Ravi Ramakrishna   Building Infinite Ray-Class Towers with Specific Signatures and Small Bounded Root Discriminant
Melanie Pivarski   Laurent Saloff-Coste   Heat Kernels on Euclidean Complexes
Franco Saliola   Kenneth Brown   The Face Semigroup Algebra of a Hyperplane Arrangement
Steven Sinnott   Michael Stillman   Results in Computational Algebra of Bayesian Networks
Brigitta Vermesi   Gregory Lawler   Intersection Exponents for Random Walks on Cylinders
May 2006        
Student   Advisor   Dissertation
Jeffrey Abraham Mermin   Michael Stillman   Lexicographic Ideals
John Thacker   Gregory Lawler   Properties of Brownian and Random Walk Loop Soups
January 2006        
Student   Advisor   Dissertation
Steven Morris   Reyer Sjamaar   Four- and Six-Dimensional Nilmanifolds and Symplectic Forms
Yan Zeng   Philip Protter   Compensators of Stopping Times
August 2005        
Student   Advisor   Dissertation
Maria Belk   Robert Connelly   Applications of Stress Theory: Realizing graphs and Kneser-Poulsen

Nathanael Berestycki

  Richard Durrett   Phase Transitions for the Distance of Random Walks with Applications to Genome Rearrangements
Lee Gibson   Laurent Saloff-Coste   The Number of Sites Visited By a Random Walk on an Infinite Graph
Radu Haiduc   John Guckenheimer   Horseshoes in the Forced van der Pol Equation
Spencer Hamblen   Ravi Ramakrishna   Lifting n-dimensional Galois Representations
Christopher Hardin   Dexter Kozen   The Horn Theory of Relational Kleene Algebra
Todd Kemp   Leonard Gross   Hypercontractivity in Non-commutative Holomorphic Spaces
Antonio Montalban   Richard Shore   Beyond the Arithmetic
Roland Roeder   John Hubbard   Topology for the Basins of Attraction of Newton’s Method in Two Complex Variables
Hasanjan Sayit   Philip Protter   Realistic No Arbitrage Condition
Serguei Slavnov   Anil Nerode   Semantic Investigations of Linear Logic
José Trujillo Ferreras   Gregory Lawler   The Random Walk Loop Soup and the Expected Area of the Brownian Loop in the Plane
Russell Woodroofe   Kenneth Brown   Shelling the Coset Poset
May 2005        
Student   Advisor   Dissertation
Fernando Schwartz   José Escobar   Scalar Curvature Problems on Manifolds with Boundary
August 2004        
Student   Advisor   Dissertation
James Belk   Kenneth Brown   Thompson's Group F
Nelia Charalambous   José Escobar   On the L^p Independence of the Spectrum of the Hodge Laplacian and Logarithmic Sobolev Inequalities on Non-Compact manifolds
Dan Ciubotaru   Dan Barbasch   Unitary Representations of Exceptional p-adic Groups
Jean Cortissoz   José Escobar   On the Ricci Flow in Rotationally Symmetric Manifolds with Boundary
Christopher Francisco   Michael Stillman  

Hilbert functions and graded free resolutions

Yuval Gabay   Richard Shore   Double Jump Inversions and Strong Minimal Covers in the Turing Degrees
Noam Greenberg   Richard Shore   The Role of True Finiteness in the Admissible Recursively Enumerable Degrees
JaEun Ku   Lars Wahlbin   Least-Squares Methods for Second-Order Elliptic Partial Differential Equations
Dmitry Leykekhman   Lars Wahlbin   Pointwise Weighted Error Estimates for Parabolic Finite Element Equations
Yi Lin   Reyer Sjamaar   Equivariant Symplectic Hodge Theory and Strong Lefschetz Manifolds
Harrison Huibin Zhou   J. T. Gene Hwang &
Michael Nussbaum
  Minimax Estimation with Thresholding and Asymptotic Equivalence for Gaussian Variance Regression
May 2004        
Student   Advisor   Dissertation
Shawn Walker   Louis Billera   Shift Techniques and Multicover Inequalities on Colored Complexes
January 2004        
Student   Advisor   Dissertation
Janet Best   Richard Durrett   The Mathematics of Ecological Competition
August 2003        
Student   Advisor   Dissertation
Matthew Eugene Horak   Karen Vogtmann   Mapping Class Subgroups of Outer Automorphism Groups of Free Groups
Samuel K. Hsiao   Louis Billera   Peak Quasisymmetric Functions and Flag Enumeration in Eulerian Posets
Fernando Codá Marques   José Escobar   Existence and Compactness Theorems on Conformal Deformation of Metrics
Reba Schuller   Anil Nerode   A Theory of Multitask Learning for Learning from Disparate Data Sources
August 2002        
Student   Advisor   Dissertation
Ryan Budney   Allen Hatcher   Representations of Mapping Class Groups via Topological Constructions
Alan Robert Demlow   Lars Wahlbin   Estimates for and Properties of Mixed Finite Element Methods for Elliptic Problems
Ferenc Gerlits   Karen Vogtmann   Invariants in Chain Complexes of Graphs
Leah Gold   Michael Stillman   Homological Results in Commutative Algebra
Geoffrey Christopher Hruska   Karen Vogtmann   Nonpositively Curved Spaces with Isolated Flats
Suzanne Lynch Hruska   John Smillie   Hyperbolicity in the Complex Henon Family
Swapneel Mahajan   Kenneth Brown   Shuffles and Shellings via Projection Maps
Joseph Miller   Anil Nerode   Co-computably Enumerable Classes in Computable Analysis and Topology
David Revelle   Laurent Saloff-Coste   Random Walks on Solvable Groups
May 2002        
Student   Advisor   Dissertation
Sarah Agnes Spence   Dextor Kozen and Stephen Wicker   Subspace Subcodes and Generalized Coset Codes
August 2001        
Student   Advisor   Dissertation
David Anthony Brown   John Hubbard   Using Spider Theory to Explore Parameter Spaces
Kathryn Louise Nyman   Louis Billera   Enumeration in Geometric Lattices and the Symmetric Group