Recent Graduates
Past Dissertations
The following list of dissertation titles suggests the range of research interests pursued by graduate students in the Department of Mathematical Sciences.
2011
Rita Goncalves Ferreira
Spectral and Homogenization Problems
Entry Position: Postdoctoral Fellow, Univ. Nova de Lisboa, Portugal
Advisor: Irene Fonseca and M. Luisa Mascarenas (Portugal)
Michael Klipper
Analysis for the Beginning Mathematician (Doctor of Arts)
Entry Position: Lecturer, Math Dept., Univ. Georgia, Athens
Advisor: John Mackey
Peter Lumsdaine
Higher Categories from Type Theories
Entry Position: Postdoctoral Fellow, Dalhousie University, Canada
Advisor: Steve Awodey
Silviu Predoiu
Optimal Execution in a General One-Sided Limit-Order Book and Endogeneous Dynamic Completeness of Financial Models
Entry Position: Citigroup, New York
Advisor: Dmitry Kramkov
Reshma Ramadurai
On Induced Vertex Folkman Numbers
Entry Position: Postdoctoral Fellow, Computer Science Dept., Masaryk Univ., Czech Republic
Advisor: Andrzej Dudek
Pietro Siorpaes
Marginal Prices, Optimal Investment and Sobolev Parametric Martingales
Entry Position: Postdoctoral Fellow, Math Dept., Univ. Vienna, Austria
Advisor: Dmitry Kramkov
Daniel Spector
Characterization of Sobolev and BV Spaces
Entry Position: Research Fellow, Math Dept., Zhejiang Univ., Hungszhou, China
Advisor: Giovanni Leoni
Matthew Szudzik
Some Applications of Recursive Functionals to the Foundations of Mathematics and Physics
Entry Position: Assistant Teaching Prof., Carnegie Mellon Qatar Campus
Advisor: Rick Statman
Zelealem Yilma
Results in Extremal Graph and Hypergraph Theory
Entry Position: Postdoctoral Fellow, Univ. Paris, France
Advisor: Oleg Pikhurko
Hang Yu
Horizon Dependence of Utility Optimizers in Incomplete Models
Entry Position: Associate Vice-President, ETG Dept., Knight Capital Group, New Jersey
Advisor: Kasper Larsen
2010
Maxim Bichuch
Asymptotic Analysis for Optimal Investment and Consumption with Transaction Costs with Two Futures Contracts
Advisor: Steven Shreve
Entry Position: Postdoctoral Research Associate, Operations Research & Financial Eng. Dept., Princeton Univ., New Jersey
Brian Seguin
Frame-Free Continuum Thermodynamics
Advisor: Walter Noll
Entry Position: Postdoctoral Researcher, Math and Statistics Dept., McGill Univ., Canada
Christopher Wallace
Mixed Integer Program Heuristics
Advisor: Egon Balas
Entry Position: Assistant Prof., Computer and Information Sciences, East Tennessee State Univ.
Anne Yust
Data Driven Modeling and Intervention Design in Large Biological Systems
Advisor: Shlomo Ta’asan
Entry Position: Assistant Professor, Dept. of Mathematics, Birmingham Southern College, Alabama
2009
Pall Melsted
Algorithms on Random Graphs
Advisor: Alan Frieze
Entry Position: Programmer, Human Genetics, Univ. of Chicago, IL
Fritz Obermeyer
Automated Equational Reasoning in Nondeterministic Lambda-Calculi Modulo Theories H-*
Advisor: Richard Statman
Entry Position: Research Analyst, Toyon Research Corp., California
David Offner
Extremal Problems on the Hypercube
Advisor: Oleg Pikhurko
Entry Position: Assistant Prof., Math Dept., Westminster College, PA
Alexander Rand
Delaunay Refinement Algorithms for Numerical Methods
Advisor: Noel Walkington
Entry Position: Postdoctoral Fellow, Inst. Computational Eng. & Sciences, Univ. Texas Austin
Karl Wimmer
Fourier Methods and Combinatorics in Learning Theory
Advisor: Ryan O’Donnell
Entry Position: Assistant Prof., Comp. Sci. & Statistics Dept., Duquesne University, PA
2008
Barbara Anthony
Approximation Algorithms for Network Design with Uncertainty
Advisor: Anupam Gupta
Entry Position: Assistant Prof., Computer Science Dept., Southwestern University, Texas
Danut Arama
On a Variational Approach for Stokes Conjectures in Water Waves
Advisor: Giovanni Leoni
Entry Position: Postdoctoral Fellow, Math & Statistics Dept., Loyola University, Illinois
Gerard Brunick
A Weak Existence Result with Application to the Financial Engineer’s Calibration Problem
Advisor: Steven Shreve
Entry Position: Lecturer, Math Dept., Univ. of Texas Austin
Prasad Chebolu
Topics in Random Graphs
Advisor: Alan Frieze
Entry Position: Research Associate, Computer Science Dept., Univ. of Liverpool, UK
David German
Corrections to the Prices of Derivatives Due to Market Incompleteness and Price Impact
Advisor: Dmitry Kramkov
Entry Position: Assistant Prof., Math Dept., Claremont McKenna College, California
Michael Picollelli
Extremal Problems and Random Processes on Graphs
Advisor: Thomas Bohman
Entry Position: Supplemental Faculty, Math Sciences Dept., Univ. of Delaware
Bernardo Sousa
Variational Methods for Phase Transitions
Advisors: Irene Fonseca and Giovanni Leoni
Entry Position: Postdoctoral Fellow, Math & Statistics Dept., McMaster Univ., Canada
Henry Towsner
Some Results in Logic and Ergodic Theory
Advisor: Jeremy Avigad
Entry Position: Postdoctoral Fellow, Math Sciences Research Inst., Berkeley, CA
Michael Young
Triangle Problems in Extremal Graph Theory
Advisors: James Cummings and John Mackey
Entry Position: Postdoctoral Fellow, Math & Statistics Dept., Smith College, Mass.
2007
Graca Carita
Relaxation in SBV for Constrained-valued Fields
Advisors: Irene Fonseca and Giovanni Leoni
Entry Position: Assistant Prof., University Evora, Portugal
Albert Cohen
A Probabilistic Analysis of Two Dimensional Grain Growth
Advisor: David Kinderlehrer
Entry Position: Postdoctoral Fellow, Math Dept., Michigan State Univ.
2006
Kelley Burgin
Hamilton Cycles in Random Graphs
Advisor: Alan Frieze
Entry Position: Applied Research Mathematician, Dept. of Defense, Maryland
Milica Cudina
Asymptotically Optimal Control for Some Time-Varying Stochastic Networks
Advisors: Steven Shreve and Kavita Ramanan
Entry Position: Lecturer, Math Dept., Univ. of Texas Austin
Abraham Flaxman
Average-Case Analysis for Combinatorial Problems
Advisor: Alan Frieze
Entry Position: Theory Group, Microsoft Research, Washington
Sean Hilden
Allocation of Risk Capital via Intra-Firm Trading
Advisor: David Heath
Entry Position: Associate, Model Validation, Lehman Brothers, New York
Anatoli Karolik
Modeling Correlated Credit Rating Migrations
Advisor: Steven Shreve
Entry Position: Associate, Credit Derivatives, Bank of Nova Scotia
David Kravitz
Satisfiability and the Giant Component in Online Variants of the Classical Random Models
Advisor: Alan Frieze
Entry Position: Applied Mathematician, National Security Agency, Maryland
Venkatesh Natarajan
Independent Sets in Powers of Odd Cycles and the Global Min-Cut Problem
Advisor: Thomas Bohman
Entry Position: Research Software Scientist, Google, New York
Juan Vera
Variations on the Preferential Attachment Graph
Advisors: Alan Frieze and Javier Pena
Entry Position: Postdoctoral Fellow, Computer Science Dept., Georgia Tech
2005
Konstantin Andreev
Approximation Algorithms for Network Design and Graph Partitioning Problems
Advisor: Bruce Maggs
Entry Position: Consultant, Pricing Analytics, Chatham Financial, PA
Margarida Baia
Variational Multiscale Problems and Applications to Thin Films
Advisor: Irene Fonseca
Entry Position: Professor Auxiliar, Math Dept., Instituto Superior Tecnico, Portugal
Stephen D’Silva
Time Consistent and Currency Invariant Risk Adjusted Valuations
Advisor: David Heath
Entry Position: Associate, Fixed Income Research, Lehman Brothers, New York
Caner Kazanci
Statistical Analysis and Reverse Engineering of Large Biochemical Networks
Advisor: Shlomo Ta’asan
Entry Position: Assistant Professor, Math & Engineering Dept., Univ. of Georgia
Stephen Pankavich
The Vlasov-Poisson System with Infinite Mass and Energy
Advisor: Jack Schaeffer
Entry Position: Postdoctoral Fellow, Math Dept., Indiana Univ.
Traian Pirvu
Maximizing Portfolio Growth Rate under Risk Constraints
Advisor: Steven Shreve
Entry Position: Postdoctoral Fellow, Math Dept., Univ. British Columbia
Cristina Popovici
Coupled Singular Perturbations and Homogenization in Phase Transitions
Advisor: Irene Fonseca
Entry Position: Visiting Postdoctoral Fellow, Math Dept., University of Utah
Adam Speight
Multigrid Methods for Calibrating Financial Models
Advisor: Shlomo Ta’asan
Entry Position: Assistant Prof., Risk Management and Insurance, Georgia State Univ.
Adrian Tudorascu
Optimal Mass Transportation Methods for Gradient Flows in the Weak Topology
Advisor: David Kinderlehrer
Entry Position: Postdoctoral Fellow, Math Dept., Georgia Tech Univ.
Aris Winger
On Pattern Formation in a One Dimensional Viscoelastic System with Numerical Computation
Advisors: William Hrusa and Roy Nicolaides
Entry Position: Assistant Prof., Math and Computer Sci. Dept., Emory and Henry College, Virginia
2004
Marian Bocea
A Young Measure Approach to Nonlinear Membrane Theory
Advisor: Irene Fonseca
Entry Position: Visiting Assistant Prof., Math Dept., Univ. of Utah
Chad Brown
Set Comprehension in Church’s Type Theory
Advisor: Peter Andrews
Entry Position: Postdoctoral Fellow, Universitat des Saarlandes, Germany
Karel Janecek
Futures Trading Model with Transaction Costs
Advisor: Steven Shreve
Entry Position: Research Scientist, Radon Institute, Austria
Olexei Kolesnikov
Generalized Amalgamation in Simple Theories and Characterization of Dependence in Non-Elementary Cases
Advisor: Rami Grossberg
Entry Position: Visiting Assistant Prof., Math Dept., Univ. of Michigan, Ann Arbor
Paul Komarek
Logistic Regression for Data Mining and High-Dimensional Classification
Advisor: Andrew Moore
Entry Position: Postdoctoral Fellow, Robotics Inst, Carnegie Mellon Univ.
Kerry Ojakian
Combinatorics in Bounded Arithmetic
Advisor: Jeremy Avigad
Entry Position: Postdoctoral Fellow, Faculty of Math & Physics, Charles University, Czech Republic
Luca Petrelli
Variational Principle for General Diffusion Problems
Advisor: David Kinderlehrer
Entry Position: Assistant Prof., Math & Comp. Sci. Dept., Mount St. Mary’s Univ., Maryland
Petronella Radu
On Semilinear Wave Equations
Advisor: Luc Tartar
Entry Position: Assistant Prof., Math Dept., Univ. Nebraska, Lincoln
Juan Rivera
Portfolio Choice under Risk Limits: A Coherent Approach
Advisor: Dmitry Kramkov
Entry Position: Assistant Vice President, Risk Analytics, Pittsburgh National Corp.
Ksenija Simic
Aspects of Ergodic Theory in Subsystems of Second-Order Arithmetic
Advisor: Jeremy Avigad
Entry Position: Postdoctoral Fellow, Math Dept., Univ. Arizona, Tucson
Mihai Sirbu
A Two-Person Game for Pricing Convertible Bonds
Advisor: Steven Shreve
Entry Position: Assistant Professor, Math Dept., Columbia Univ., New York
Kathryn Trapp
A Class of Compatible Discretizations with Applications to Div-Curl Systems
Advisor: Roy Nicolaides
Entry Position: Assistant Prof., Math & Comp. Sci. Dept., Univ. of Richmond, Virginia
Mingxin Xu
Minimizing Shortfall Risk Using Duality Approach – An Application to Partial Hedging in Incomplete Markets
Advisor: Steven Shreve
Entry Position: Assistant Prof., Math Dept., Univ. North Carolina, Charlotte
2003
Geoffrey Atkinson
b-independent Sets in Random Graphs
Advisor: Alan Frieze
Entry Position: Assistant Prof., Math Dept., Seton Hill Univ., PA
John Krueger
Saturated Ideals
Advisor: James Cummings
Entry Position: Postdoctoral Fellow, Kurt Godel Research Center for Math Logic, Austria
Steven Pav
Delaunay Refinement Algorithms
Advisor: Noel Walkington
Entry Position: Visiting Assistant Prof., Math Dept., Univ. California, San Diego
Pedro Santos
On Some Constrained Variational Problems
Advisor: Irene Fonseca
Entry Position: Assistant Prof., Math Dept., Instituto Superior Tecnico, Portugal
Peng Yu
Bridging Scales in Fluids and Materials Science
Advisor: Shlomo Ta’asan
Entry Position: Assistant Prof., Math Dept., Penn State Univ.
2002
Daniil Bunimovich
Modeling and Pricing of Collateralized Debt Obligations
Advisor: Steven Shreve
Entry Position: Associate Math Researcher, Credit Trading & Structuring, Bank of Nova Scotia
Jianping Liu
Molecular Models for Fluid Mixtures and Their Large Scale Dynamics
Advisor: Shlomo Ta’asan
Entry Position: Senior Application Engineer, Oracle Corp., New York
Ojas Parekh
Polyhedral Techniques for Graphic Covering Problems
Advisor: Ramamoorthi Ravi
Entry Position: Assistant Prof., Math & Comp. Sci. Dept., Emory University, Georgia
Monica VanDieren
Categoricity and Stability in Abstract Elementary Classes
Advisor: Rami Grossberg
Entry Position: Assistant Prof., Math Dept., Stanford University, California
2001
Mikil Foss
On Lavrentiev’s Phenomenon
Advisors: William Hrusa and Victor Mizel
Entry Position: Visiting Associate Prof., Math Sciences, Carnegie Mellon University
Bjarni Halldorsson
Algorithms for Biological Sequence Problems
Advisor: Ramamoorthi Ravi
Entry Position: Computer Scientist, Informatics Research, Maryland
2000
Yuri Greenfield
Hedging of the Credit Risk Embedded in Derivative Transactions
Advisor: John Lehoczky
Entry Position: Research Analyst, Derivatives Research Dept., Lehman Brothers, New York
Diego Jara
An Extension of Levy’s Theorem and Applications to Financial Models Based on Futures Prices
Advisor: David Heath
Entry Position: Associate, Fixed Income Derivatives, Lehman Brothers, New York
Aggelos Tsikas
Solid State Mass Diffusion with Crystalline Interfacial Energy
Advisor: Morton Gurtin
Entry Position: Postdoctoral Fellow, Applied Math Dept., National Technical Univ., Athens, Greece
Feyzullah Egriboyun
Optimal Investment and Consumption with Reallocation and Drawdown Constraints
Advisor: Mete Soner
Entry Position: Developer/Modeler, Global Mode and Analytics, CS First Boston Corp., New York
Goran Konjevod
Generalizing Set Cover: Approximation Algorithms for Group Steiner Trees and Related Problems
Advisor: Ramamoorthi Ravi
Entry Position: Assistant Prof., Computer Sci. & Engineering Dept., Arizona State Univ.
Jan Vecer
Options on a Traded Account
Advisor: Steven Shreve
Entry Position: Visiting Assistant Prof., Univ. of Michigan, Ann Arbor
1999
Matthew Bishop
Mating Search without Path Enumeration
Advisor: Peter Andrews
Entry Position: Research Associate, Computing Dept., Imperial College, UK
Jeffery Boats
Linear Algebra Textbook Implementing Instructional Technology
Advisor: Richard MacCamy
Entry Position: Assistant Prof., Dept. Math & Comp. Sci., Univ. Detroit Mercy, Michigan
Byungduck Chough
Numerical Techniques for Macroscopic Dynamics of Particle Systems: Dilute Gases
Advisor: Shlomo Ta’asan
Entry Position: Senior Technical Member, Network Maintenance Solutions, AT&T, New Jersey
Roberto Virga
Higher-Order Rewriting with Dependent Types
Advisor: Frank Pfenning
Entry Position: Postdoctoral Research Associate, Computer Science Dept., Princeton Univ., New Jersey
Lei Zhao
Disjoint Paths in Random Graphs
Advisor: Alan Frieze
Entry Position: Software Design Engineer, Microsoft Corp., Washington
1998
Olivier Lessmann
Dependence Relations in Non-elementary Classes
Advisor: Rami Grossberg
Entry Position: Research Assistant Prof., Math Dept., Univ. Illinois, Chicago
Neil Simonetti
Applications of a Dynamic Programming Approach to the Traveling Salesman Problem
Advisor: Egon Balas
Entry Position: Assistant Prof., Math/Science Dept., Bryn Athyn College of the New Church, PA
Dennis Wong
A Unifying Credit Model
Advisor: Steven Shreve
Entry Position: Research Assistant, Research and Advising Services, Scotia Capital Markets, Canada
Uwe Wystup
Valuation of Exotic Options under Short-selling Constraints
Advisor: Steven Shreve
Entry Position: Product and Modeling Specialist, Foreign Exchange Options Div., Sal.Oppenheim Jr. & CIE, Germany
Hongwei Xi
Dependent Types in Practical Programming
Advisor: Frank Pfenning
Entry Position: Assistant Prof., Electrical & Computer Eng. & Comp. Sci. Dept., Univ. Cincinnati, Ohio
Andrew Yershov
Numerical Methods for the Shallow Water Equations
Advisor: James Greenberg
Entry Position: Actuarial Assistant, Insurance Services Office, New York
1997
George Christopher
Structure and Applications of Totally Decomposable Metrics
Advisor: Michael Trick
Entry Position: Assistant Prof., Math & Statistics Dept., Rochester Inst. Tech., New York
Bogdan Doytchinov
Heavy Traffic Limits of Queues with Due Dates
Advisor: Steven Shreve
Entry Position: Postdoctoral Associate, Math Sciences Dept., Carnegie Mellon
Sergio Gutierrez
Laminations in Linearized Elasticity and a Lusin Type Theorem for Sobolev Spaces
Advisor: Luc Tartar
Entry Position: Assistant Prof., Math Dept., Pont. Universidad Catolica de Chile
Raul Kangro
Analysis of Artificial Boundary Conditions for Black-Scholes Equations
Advisor: Roy Nicolaides
Entry Position: Senior Researcher, Math Dept., Tartu University, Estonia
Urve Kangro
Spurious Fields in Computational Electromagnetics
Advisor: Roy Nicolaides
Entry Position: Senior Researcher, Math Dept., Tartu University, Estonia
Priyantha Perera
Liquid Diffusion Couple in a Microgravity Environment
Advisor: Robert Sekerka
Entry Position: Quantitative Application Developer, FactSet Research Systems, Inc., Connecticut
Stephen Watson
Unique Global Solvability for Initial-Boundary Value Problems in One-Dimensional Nonlinear
Thermoviscoelasticity with Phase Transitions
Advisor: William Hrusa
Entry Position: Assistant Prof., Math Dept., Univ. Louisiana, Baton Rouge
Gregor Weiske
On Some Problems Related to Linear Elasticity, Optimal Design and Homogenization
Advisor: Luc Tartar
1996
Hui Chen
On Some Problems of Hypergraphs
Advisor: Alan Frieze
Entry Position: Quantitative Strategist, Fixed Income Research, Credit Suisse First Boston, New York
Christopher Larsen
Variational and Measure Theoretic Techniques for Material Equilibria
Advisor: Irene Fonseca
Entry Position: Visiting Assistant Prof., Math Sciences Dept., Worcester Polytechnic Inst., Mass.
Da-qing Wang
Applications of the Co-volume Method in Computational Electromagnetics
Advisor: Roy Nicolaides
Entry Position: Postdoctoral Fellow, Math Sciences Dept., Univ. Delaware, Newark
Han Wang
Numerical Solution of a Non-convex Optimization Problem Modeling Martensitic Microstructure
Advisor: Roy Nicolaides
Entry Position: Visiting Assistant Prof., Math Dept., Univ. of North Carolina, Charlotte
1995
Jonathan Aronson
Analysis of a Randomized Greedy Matching Algorithm
Advisor: Alan Frieze
Entry Position: Center for Computing Sciences, Bowie, Maryland
Robert Carr
Polynomial Separation Procedures and Facet Determination for Inequalities of the Traveling Salesman Polytope
Advisors: Egon Balas and Gerald Thompson
Entry Position: Postdoctoral Fellow, Grad School of Industrial Administration, Carnegie Mellon Univ.
Dmitry Golovaty
The Volume Preserving Motion by Mean Curvature as an Asymptotic Limit of Reaction-Diffusion Equations
Advisor: Mete Soner
Entry Position: Assistant Prof., Math & Comp. Sci. Dept., Univ. Akron, Ohio
Romaine Jayewardene
Relations and Functional Relations in Categories with Examples from Fuzzy Set Theory
Advisor: Oswald Wyler
Entry Position: Lecturer, University of Colombo, Sri Lanka
Michel Schellekens
The Smyth Completion: A Common Topological Foundation for Denotational Semantics and Complexity Analysis
Advisor: Stephen Brookes
Entry Position: Postdoctoral Researcher, Dept. of Computing, Imperial College, UK
1994
Ana Barroso
Variational Methods for Phase Transitions
Advisor: Irene Fonseca
Entry Position: Assistant Prof., Math Dept., Univ. Lisboa, Portugal
Michael Molloy
Random Graphs with a Fixed Degree Sequence
Advisor: Alan Frieze
Entry Position: Postdoctoral Fellow, Computer Science Dept., Univ. Toronto, Canada
Dmitry Pugachevsky
A Stochastic Control Problem for Nematic Liquid Crystals with Variable Degree of Orientation
Advisor: Victor Mizel
Entry Position: Associate, Global Investment Banking, Bankers Trust Co., New York
W. Dow Rieder
An Optimal Algorithm for the Construction of Voronoi-Delaunay Mesh Systems in General Domains
Advisor: Roy Nicolaides
Kristina Vuskovic
On Balanced Bipartite Graphs
Advisor: Gerard Cornuejos
Entry Position: Postdoctoral Fellow, Combinatorics & Optimization Dept., University of Waterloo, Canada
