# 2023

**Zhijun Chen*** Conditioning of Random Feature Matrices and Sparse Recovery*

Advisor: Hayden Schaeffer

Entry Position: Postdoctoral Fellow, NIH, Bethesda, MD

**Zichao Dong*** Several problems in extremal combinatorics*

Advisor: Boris Bukh

Entry Position: Postdoctoral Research Fellow, Institute for Basic Science - Extremal Combinatorics and Probability Group, Daejeon, South Korea

**Junichi Koganemaru*** Traveling wave solutions to the free boundary Navier-Stokes equations*

Advisor: Ian Tice

Entry Position: Visiting Professor, Carnegie Mellon University, Pittsburgh

**Samson Leung*** Stability, Categoricity and Axiomatization of Abstract Elementary Classes*

Advisor: Rami Grossberg

Entry Position: Assistant Teaching Professor, Penn State University, State College, PA

**Anish Sevekari*** Probabilistic Analysis of Various Algorithms*

Advisor: Wesley Pegden

Entry Position: Postdoctoral Fellow in Computational Biology, University of Pittsburgh, Pittsburgh, PA

**Yifan Sun*** Topics on modeling high dimensional time series data*

Advisor: Hayden Schaeffer

Entry Position: Algo Quant, Barclays Capital, New York, NY

**Yukun Yue*** Convergence Analysis Of Numerical Schemes For Liquid Crystals Based On The Invariant Energy Quadratization Method*

Advisor: Franziska Weber

Entry Position: Van Vleck Visiting Assistant Professor, University of Wisconsin-Madison, Madison, Wisconsin

**Zeyu Zhang*** Propagation of chaos for order statistics of particle systems with mean-field interaction*

Advisor: Martin Larsson

Entry Position: Associate, Quantitative Strategist, Goldman Sachs, New York, NY

# 2022

**Charles Argue*** Chasing Convex Bodies and Functions*

Advisor: Anupam Gupta

Entry Position: Lecturer at Yale University, New Haven, CT

**Kayla Bollinger*** Reduced Order Models and Regression for Applications to Structural Modeling*

Advisor: Hayden Schaeffer

**Hanif Cheung***Notions of Amalgamation for Abstract Elementary Classes*

Advisor: Rami Grossberg

Entry Position: Associate, Fixed Income Division, Quantitative Finance, Morgan Stanley & Co. International PLC., London, UK

**Likhit Ganedi***Applications of Two Scale Gamma Convergence to Composite Non-Classical Materials*

Advisor: Irene Fonseca

Entry Position: Postdoctoral Research Associate, Aachen University, Germany

**Mihir Abhay Hasabnis***Topics in Extremal Structures and Random Graphs*

Advisor: Alan Frieze

Entry Position: Postdoctoral Associate at Indian Institutes of Science Education and Research (IISER), Pune, India

**Won Eui Hong***Convergence Problems in Nonlocal Dynamics with Nonlinearity*

Advisor: Robert Pego

**David Itkin***Growth Optimization in Stochastic Portfolio Theory with Applications to Robust Finance and Open Markets*

Advisor: Martin Larsson

Entry Position: Chapman Fellow, Department of Mathematics at Imperial College London, London, UK

**Oleksandr Rudenko***Topics in Network and Market Optimization*

Advisor: R. Ravi

Entry Position: Jane Street Capital, New York, NY

# 2021

**Shaun Allison*** Orbit Equivalence Relations and Anticlassification Results*

Advisor: Clinton Conley

Entry Position: Postdoctoral Associate, Einstein Inst. of Math, Hebrew Univ. of Jerusalem

**Da Qi Chen*** Topics in Information Dissemination, Network Fortification and Extremal Structures*

Advisor: R. Ravi

Entry Position: Postdoctoral Research Assistant at University of Virginia Biocomplexity Institute and Initiative, Charlottesville, VA

**Mochong Duan*** Numerical Approximations of Viscoelastic Fluids*

Advisor: Noel Walkington

Entry Position: Quantitative Associate, Goldman Sachs, New York, NY

**Sittinon Jirattikansakul*** Blowing up the power of a singular cardinal of any cofinality with collapses*

Advisor: James Cummings

Entry Position: Postdoctoral Associate, Tel Aviv University

**Marcos Mazari Armida*** Remarks on classification theory for abstract elementary classes with applications to abelian group theory and ring theory*

Advisor: Rami Grossberg

Entry Position: Burnett Meyer Postdoctoral Fellow, University of Colorado Boulder, Boulder, Colorado

**Han Nguyen*** Adaptive optimization methods for machine learning*

Advisors: Barnabás Póczos & Shlomo Ta'asan

Entry Position: Machine Learning Engineer, Comcast, Philadephia, PA

**Matthew Superdock*** Topics in topological combinatorics: Simplicial complexes, finite geometries, and the topology of circle-valued maps*

Advisor: Florian Frick

Entry Position: Visiting Assistant Professor of Computer Science, Rhodes College, Memphis, TN

**Son Van*** Investigations of the dynamics of models of heat transfer and clustering*

Advisors: Gautam Iyer and Robert Pego

Entry Position: Hans Rademacher instructor, University of Pennsylvania, Philadelphia, PA

**Kerrek Stinson*** Analysis of a Variational Model for Lithium-Ion Batteries*

Advisors: Irene Fonseca and Giovanni Leoni

Entry Position: Postdoctoral Fellow, University of Bonn, Bonn, Germany

**Ananya Uppal*** Nonparametric Density Estimation under Dual Besov Norms*

Advisor: Barnabás Póczos

Entry Position: Postdoctoral Fellow, University of Texas at Austin

# 2020

**Debsoumya Chakraborti*** Topics in extremal and random discrete structures*

Advisor: Po-Shen Loh

Entry Position: Postdoctoral Researcher, Institute for Basic Science, Daejeon, South Korea

**Christopher Cox*** Problems in coding theory and extremal combinatorics*

Advisor: Boris Bukh

Entry Position: RTG Postdoctoral Research Associate, Iowa State University, Ames, IA

**Ilqar Ramazanli*** Optimal Adaptive Matrix Completion*

Advisor: Barnabás Póczos

Entry Position: Research Scientist, Facebook, New York, New York

**Antoine Remond-Tiedrez*** Nonlinear partial differential equations in fluid dynamics: interfaces, microstructure, and stability*

Advisor: Ian Tice

Entry Position: Van Vleck Assistant Professor, University of Madison-Wisconsin, Madison, Wisconsin

**Xiaofei Shi*** Equilibrium Asset Pricing with Transaction Costs*

Advisor: Johannes Muhle-Karbe

Entry Position: Term Assistant Professor, Department of Statistics at Columbia University, New York, New York

**Weicheng Ye*** Bandit Methods and Selective Prediction in Deep Learning*

Advisor: Shlomo Ta'asan

Entry Position: Quantitative Research for Credit Suisse, New York

# 2019

**Christopher Almost*** Diffusion Scaling of a Limit-Order Model: The Symmetric Case*

Advisor: Steven Shreve

Entry Position: Quantitative Research Analyst, Waterfront International, Toronto, Canada

**Michael Anastos*** Algorithmic and Structural Properties of Random Graphs*

Advisor: Alan Frieze

Entry Position: Postdoctoral Associate, Freie Universitat, Berlin

**Yuanyuan Feng*** Dissipation Enhancement by Mixing*

Advisor: Gautam Iyer

Entry Position: S. Chowla Assistant Professor (Postdoctoral), Penn State, State College, Pennsylvania

**Giovanni Gravina*** Variational Techniques for Water Wave and Singular Perturbations*

Advisor: Giovanni Leoni

Entry Position: Postdoctoral Associate, Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic

**David Gutman*** First-Order Methods in Convex Optimization: Acceleration, Conditioning, and Rescaling*

Advisor: Javier Pena

Entry Position: Assistant Professor, Texas Tech University, Lubbock, Texas

**Adrian Hagerty*** Variational Methods for Second Order Structured Deformations and Multiscale Problems*

Advisor: Irene Fonseca

Entry Position: Machine Learning Engineer, Edge Case Research

**Yan Xu*** An Optimal Transport Problem with Backward Martingale Constraint Motivated by Equilibrium with Insider*

Advisor: Dmitry Kramkov

Entry Position: Algorithmic Trading, Deutsche Bank, Singapore

**Xiaofeng Yu*** Diffusion Scaling of a Limit-Order Book Model: The Asymmetric Case*

Advisor: Steven Shreve

Entry Position: Research Associate, Goldman Sachs, Jersey City, New Jersey

**Jing Zhang*** Some Results in Combinatorial Set Theory*

Advisor: James Cummings

Entry Position: Postdoctoral Fellow, Israel Academy of Sciences and Humanities, Ramat Gan, Israel

**Linan Zhang*** Sparse Recovery And Deep Learning For Extracting Time-Dependent Models From Data*

Advisor: Hayden Schaeffer

Entry Position: Postdoctoral Researcher, University of Pittsburgh, Pittsburgh, PA

# 2018

**Joseph Briggs***Online Algorithms and Extremal Structures*

Advisor: Wesley Pegden

Entry Position: Postdoctoral Fellow, Technion Israel Institute of Technology, Haifa, Israel

**Samuel Cohn***On the Homogenization of Diffusions in Periodic Comb-Like Structues*

Advisors: Gautam Iyer and Robert Pego

Entry Position: Google

**Praveen Kolli***Topics in Rank-Based Stochastic Differential Equations*

Advisor: Mykhaylo Shkolnikov

Entry Position: Machine Learning Engineer, Houzz, Palo Alto, California

**Clive Newstead***Algebraic Models of Dependent Type Theory*

Advisor: Steve Awodey

Entry Position: Lecturer, Northwestern University, Evanston, IL

**Yue Pu***Weakly Singular Waves and Blow-up for a Regularization of the Shallow-water System*

Advisor: Robert Pego

Entry Position: Quantitative Associate, Goldman Sachs, New York, New York

**Jing Wang***Escrow and Clawback*

Advisor: Steven Shreve

Entry Position: Research Associate, Bank of America, New York, New York

**Andrew Zucker***New Directions in the Abstract Topological Dynamics of Polish Groups*

Advisor: Clinton Conley

Entry Position: NSF Postdoctoral Fellow, Université Paris Diderot, Paris, France

# 2017

**Arda Antikacioglu**

*Quantifying and Improving Sales Diversity in Recommender Systems*

Advisor: Ramamoorthi Ravi

Entry Position: Vice-President Portfolio Optimization and Management, WorldQuant LLC, Connecticut

**Jeff Eisenbeis**

*Nonlocal Aggregation Dynamics with Near-neighbor Weighting, and the Associated Geometry of Measures*

Advisors: Robert Pego and Dejan Slepčev

Entry Position: Software Engineer, HERE Technologies, Carlsbad, California

**Jennifer Iglesias**

*Approximation Algorithms for Faster Communication and Cheaper Networks Using Linear Programming*

Advisor: Ramamoorthi Ravi

Entry Position: Software Engineer, Waymo, Mountain View, California

**Tony Johansson**

*Random Graphs and Algorithms*

Advisor: Alan Frieze

Entry Position: Postdoctoral Fellow, Dept. of Mathematics, Uppsala Univ, Sweden

**Slav Kirov**

*Models and Methods for One-Dimensional Approximations to Point Cloud Data*

Advisor: Dejan Slepčev

Entry Position: Research Scientist at Eigen Technologies, London UK

**Mikhail Lavrov**

*Results in Ramsey Theory and Probabilistic Combinatorics*

Advisor: Po-Shen Loh

Entry Position: Postdoctoral Fellow, College of Engineering, University of Illinois and Urbana

**Pan Liu**

*Variational and Partial Differential Equation Methods for Impage Processing*

Advisor: Irene Fonseca

Entry Position: Research Associate, Math Dept., University of Cambridge, UK

**Thomas Murphy**

*Convex Analysis of an Equation Arising in Oil Reservoir Models*

Advisor: Noel Walkington

Entry Position: Quantitative Researcher, Volant Trading, New York

**Matteo Rinaldi**

*Dynamics of Phase Separation and Pattern Formation*

Advisors: Irene Fonseca and Giovanni Leoni

Entry Position: Consultant, Viome, New York

**Sebastien Vasey**

*Superstability and Categoricity in Abstract Elementary Classes*

Advisor: Rami Grossberg

Entry Position: Benjamin Pierce Fellow, Math Dept., Harvard University, Mass.

# 2016

**Zhe Cheng**

*Endogenous Mortgage Current Coupons*

Advisor: Scott Robertson

Entry Position: Associate, Fixed Income Division, Morgan Stanley and Co., New York

**Jacob Davis**

*Universal Graphs at $\aleph_{\omega_1+1}$ and Set-theoretic Geology*

Advisor: James Cummings

Entry Position: Programmer, Search Dept., Google, Zurich, Switzerland

**Tetsuya Ishikawa**

*Optimal Investment and Pricing in Models Where the Underlying Asset May Default*

Advisor: Scott Robertson

Entry Position: Associate, Strats Dept., Morgan Stanley and Co., New York

**Zilin Jiang**

*Problems in Discrete Geometry and Extremal Combinatorics*

Advisor: Boris Bukh

Entry Position: Postdoctoral Research Fellow, Math Dept., Israel Institute of Technology

**Jing Liu**

*Numerical Approximation of Problems that Arise in Elasticity*

Advisor: Noel Walkington

Entry Position: Research Associate, Risk Management Dept., J.P. Morgan Chase & Co., New York

**Ryan Murray**

*Some Asymptotic Results for Phase Transition Models*

Advisor: Giovanni Leoni and Robert Pego

Entry Position: Research Assistant Professor, Math Dept., Penn State University, Pennsylvania

**Daniel Rodriguez**

*Models of R-Supercompactness*

Advisor: Ernest Schimmerling

Entry Position: Postdoctoral Associate, Math Sciences Dept., Carnegie Mellon

**Tanawit Sae-Sue**

*Radner Equilibrium in Infinite and Finite Time-Horizon Lévy Models*

Advisor: Kasper Larsen

Entry Position: Lecturer, Faculty of Commerce and Accountancy, Chulalongkorn University, Thailand

**Kimberly Weston**

*Market Stability in Non-equivalent Markets and the Martingale Property of the Dual Optimizer*

Advisor: Dmitry Kramkov

Entry Position: Postdoctoral Fellow, Math Dept., University of Texas at Austin

# 2015

**Laura Bufford**

*3D-2D Dimension Reduction of Homogenized Thin Films*

Advisor: Irene Fonseca

Entry Position: Software Developer, Epic Corp., Wisconsin

**Nicolas Garcia Trillos**

*Variational Limit of Graph Cuts on Point Clouds*

Advisor: Dejan Slepčev

Entry Position: Prager Assistant Prof., Applied Math Dept., Brown Univ.

**William Gunther**

*Some Results on Classical Semantics and Polymorphic Types*

Advisor: Richard Statman

Entry Position: Software Developer, Epic Corp., Wisconsin

**Justin Hausauer**

*Sparse Grid Combination Techniques for Solving High-Dimensional Parabolic Equations with an Application to the LIBOR Market Model*

Advisor: Roy Nicolaides

Entry Position: Quantitative Strategist, Kanerai Financial Services, New York

**Brian Kell**

*Decision Diagrams for Combinatorial Optimization and Satisfaction*

Advisor: Willem-Jan van Hoeve

Entry Position: Software Engineer, Google, Pittsburgh, PA

**Marla Slusky**

*Integrating Relaxations for Combinatorial Optimization*

Advisor: Willem-Jan van Hoeve

Entry Position: Scientist, Dynamic Science Lab, Infor Co., Cambridge, Mass.

**Lijiang Wu**

*Nonlocal Interaction Equations in Heterogeneous and Non-convex Environments*

Advisor: David Kinderlehrer and Dejan Slepčev

Entry Position: Associate, Research & Development, Goldman Sachs, New York

# 2014

**Emily Allen**

*Combinatorial Interpretations of Generalizations of Catalan Numbers and Ballot Numbers*

Advisor: Irina Gheorghiciuc

Entry Position: Business Intelligence Developer, Epic Corp., Wisconsin

**William Boney**

*Advances in Classification Theory for Abstract Elementary Classes*

Advisor: Rami Grossberg

Entry Position: Benjamin Peirce and NSF Postdoctoral Fellow, Harvard University

**Christopher Lambie-Hanson**

*Covering Matrices, Squares, Scales, and Stationary Reflection*

Advisor: James Cummings

Entry Position: Postdoctoral Fellow, Einstein Inst. of Math, Hebrew Univ. of Jerusalem

**Yuhui Ouyang**

*Numerical Approximation of Valuation Equations Incorporating Stochastic Volatility Models*

Advisor: Roy Nicolaides

Entry Position: Associate, Security Div., Goldman Sachs, New York

**Robert Simione**

*Properties of Minimizers of Nonlocal Interaction Energy*

Advisor: Dejan Slepčev

Entry Position: Head Machine Learning and Data, Waynaut Co., Italy

# 2013

**Deepak Bal**

*Colorings, Matchings and Packings in Random and Pseudo-Random Graphs*

Advisor: Alan Frieze

Entry Position: Postdoctoral Fellow, Math Dept., Ryerson Univ., Toronto, Canada

**Patrick Bennett**

*Dynamic Concentration in Some Discrete Random Processes*

Advisor: Thomas Bohman

Entry Position: Postdoctoral Fellow, Computer Science Dept., University of Toronto, Canada

**Alexandra Klimova**

*Numerical Algorithm for Options of Asian Type with Continuous Sampling*

Advisor: Roy Nicolaides

Entry Position: Associate, Bank of America, New York

**Paul McKenney**

*Forcing Axioms and the Rigidity of Corona Algebra*

Advisor: Ernest Schimmerling

Entry Position: Postdoctoral Fellow, Math Dept., Miami University, Ohio

**Christopher Potter**

*Kernel Selection for Convergence and Efficiency in Markov Chain Monte Carlo*

Advisor: Robert Swendsen

Entry Position: Systems Engineer, Information Systems, Northrop Grumman, Virginia

**Jason Rute**

*Topics in Algorithmic Randomness and Computable Analysis*

Advisor: Jeremy Avigad

Entry Position: Postdoctoral Fellow, Math Dept., Penn State Univ., University Park

**Brendan Sullivan**

*Textbook and Course Materials for 21-127 Concepts of Mathematics (Doctor of Arts)*

Advisor: Jack Schaeffer

Entry Position: Lecturer, Math Dept., Emmanuel College, Boston, MA

**Charalampos Tsourakakis**

*Mathematical and Algorithmic Analysis of Network and Biological Data*

Advisor: Alan Frieze

Entry Position: Postdoctoral Fellow, School of Science, Aalto University, Finland

**Spencer Unger**

*Some Results on the Tree Property*

Advisor: James Cummings

Entry Position: Assistant Adjunct Professor, Math Dept., Univ. California Los Angeles

# 2012

**Ashwini Aroskar**

*Limits, Regularity and Removal for Relational and Weighted Structures*

Advisor: James Cummings

Entry Position: Assistant Professor, Math Dept., Univ. of Michigan, Ann Arbor

**Elena Cristina Canepa**

*Numerical Simulations of Defaults in Large Banking Systems*

Advisor: Shlomo Ta'asan

Entry Position: University Assistant, Dept. of Math Methods and Models, Univ. Politehnica of Bucharest

**Oleksii Mostovyi**

*Necessary and Sufficient Conditions in the Problem of Optimal Investment with Intermediate Consumption*

Advisor: Dmitry Kramkov

Entry Position: Postdoctoral Fellow, Math Dept., Univ. of Texas, Austin

**Paolo Piovano**

*Evolution and Regularity Results for Expitaxially Strained Thin Films and Material Voids*

Advisor: Irene Fonseca and Giovanni Leoni

Entry Position: Postdoctoral Fellow, Faculty of Mathematics, Univ. Vienna, Austria

# 2011

**Rita Goncalves Ferreira**

*Spectral and Homogenization Problems*

Advisor: Irene Fonseca and M. Luisa Mascarenas (Portugal)

Entry Position: Postdoctoral Fellow, Univ. Nova de Lisboa, Portugal

**Michael Klipper**

*Analysis for the Beginning Mathematician* (Doctor of Arts)

Advisor: John Mackey

Entry Position: Lecturer, Math Dept., Univ. Georgia, Athens

**Peter Lumsdaine**

*Higher Categories from Type Theories*

Advisor: Steve Awodey

Entry Position: Postdoctoral Fellow, Dalhousie University, Canada

**Silviu Predoiu**

*Optimal Execution in a General One-Sided Limit-Order Book and Endogeneous Dynamic Completeness of Financial Models*

Advisor: Dmitry Kramkov

Entry Position: Citigroup, New York

**Reshma Ramadurai**

*On Induced Vertex Folkman Numbers*

Advisor: Andrzej Dudek

Entry Position: Postdoctoral Fellow, Computer Science Dept., Masaryk Univ., Czech Republic

**Pietro Siorpaes**

*Marginal Prices, Optimal Investment and Sobolev Parametric Martingales*

Advisor: Dmitry Kramkov

Entry Position: Postdoctoral Fellow, Math Dept., Univ. Vienna, Austria

**Daniel Spector**

*Characterization of Sobolev and BV Spaces*

Advisor: Giovanni Leoni

Entry Position: Research Fellow, Math Dept., Zhejiang Univ., Hungszhou, China

**Matthew Szudzik**

*Some Applications of Recursive Functionals to the Foundations of Mathematics and Physics*

Advisor: Rick Statman

Entry Position: Assistant Teaching Prof., Carnegie Mellon Qatar Campus

**Zelealem Yilma**

*Results in Extremal Graph and Hypergraph Theory*

Advisor: Oleg Pikhurko

Entry Position: Postdoctoral Fellow, Univ. Paris, France

**Hang Yu**

*Horizon Dependence of Utility Optimizers in Incomplete Models*

Advisor: Kasper Larsen

Entry Position: Associate Vice-President, ETG Dept., Knight Capital Group, New Jersey

# 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 $\mathcal{H}$**

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

**Alexei 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: Szego 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