Mathematics Alumni

Degree Awarded 2012

Advisor: Figalli
Dissertation:
Placement: NSF Postdoctoral Fellowship MIT

Advisor: Chen, De La Llave
Dissertation: ON THE ROLE OF INVARIANT OBJECTS IN APPLICATIONS OF DYNAMICAL SYSTEMS
Placement: ETH-Zurich

Advisor: Luecke
Dissertation: KNOTS IN HANDLEBODIES WITH HANDLEBODY SURGERIES
Placement: Oklahoma State

Advisor: Zitkovic
Dissertation:
Placement: Carnegie Mellon

Advisor: Vasseur
Dissertation:
Placement: Univ. of Wisconsin-Madison

Advisor: Freed
Dissertation:
Placement: Regensburg

Advisor: Caffarelli
Dissertation:
Placement: Univ. of British Columbia

Advisor: Reid
Dissertation:
Placement: Universidad Federal do Ceara

Advisor: Vishik
Dissertation: INCOMPRESSIBLE BOUSSINESQ EQUATIONS AND SPACES OF BORDERLINE BESOV TYPE
Placement: Lockheed Martin Corp.

Advisor: Keel
Dissertation:

Advisor: Helm
Dissertation:
Placement: Augustana College

Advisor: Reid
Dissertation: ARITHMETIC REFLECTION GROUPS AND CONGRUENCE SUBGROUPS
Placement: Univ. of Illinois Urbana-Champaign

Advisor: Vaaler
Dissertation: COMBINATORIAL AND PROBABILISTIC TECHNIQUES IN HARMONIC ANALYSIS
Placement: NSF Postdoctoral Fellowship UCLA

Advisor: Gordon
Dissertation:
Placement: University of Coimbra

Advisor: Helm
Dissertation:
Placement: Liberal Arts Science Academy (LASA), Austin

Advisor: Gordon
Dissertation: PRETZEL KNOTS OF LENGTH THREE WITH UNKNOTTING NUMBER ONE
Placement: Concordia University

Advisor: Sirbu
Dissertation: UTILITY MAXIMIZATION WITH CONSUMPTION HABIT FORMATION IN INCOMPLETE MARKETS
Placement: Univ. of Michigan

Advisor: Zitkovic
Dissertation: STOCHASTIC EQUILIBRIUM IN A GENERAL CLASS OF INCOMPLETE BROWNIAN MARKET ENVIRONMENTS
Placement: salesforce.com (San Francisco)

Degree Awarded 2013

Advisor: Freed
Dissertation: DIFFERENTIAL T-EQUIVARIANT K-THEORY

Advisor: Reid
Dissertation: FLEXIBILITY AND RIGIDITY OF THREE-DIMENSIONAL CONVEX PROJECTIVE STRUCTURES
Placement: UC Santa Barbara

Advisor: Caffarelli
Dissertation: REGULARITY FOR SOLUTIONS OF NONLOCAL FULLY NONLINEAR PARABOLIC EQUATIONS AND FREE BOUNDARIES ON TWO DIMENSIONAL CONES
Placement: Columbia

Advisor: Helm
Dissertation: REALIZABILITY OF TROPICAL LINES IN THE FAN TROPICAL PLANE
Placement: Greenhill School

Advisor: Figalli
Dissertation: OPTIMAL TRANSPORT, FREE BOUNDARY REGULARITY, AND STABILITY RESULTS FOR GEOMETRIC AND FUNCTIONAL INEQUALITIES
Placement: Carnegie Mellon

Advisor: Tsai
Dissertation: NUMERICAL METHODS FOR HIGHLY OSCILLATORY DYNAMICAL SYSTEMS USING MULTI SCALE STRUCTURE
Placement: Georgia Tech

Advisor: Engquist
Dissertation: TOWARDS SEAMLESS MULTISCALE COMPUTATIONS
Placement: Courant

Advisor: Engquist
Dissertation: APPROXIMATION OF THE 2D COMPLEX EIKONAL EQUATION: ANALYSIS AND SIMULATION

Advisor: Knopf
Dissertation: ON THE BLOW-UP OF FOUR-DIMENSIONAL RICCI FLOW SINGULARITIES
Placement: Stanford

Advisor: Zariphopoulou
Dissertation: ESSAYS ON ACHIEVING INVESTMENT TARGETS AND FINANCIAL STABILITY
Placement: US Department of the Treasury

Advisor: Gordon
Dissertation: BEHAVIOR OF KNOT FLOER HOMOLOGY UNDER CONWAY AND GENUS TWO MUTATION
Placement: Rice

Advisor: Allcock
Dissertation: FUCHSIAN GROUPS OF SIGNATURE (0:2,...,2;1;0) WITH RATIONAL HYPERBOLIC FIXED POINTS
Placement: University of Nevada, Reno

Advisor: Caffarelli
Dissertation: REGULARITY OF A SEGREGATION PROBLEM WITH AN OPTIMAL CONTROL OPERATOR
Placement: Purdue

Advisor: Vaaler
Dissertation: RESULTANTS AND HEIGHT BOUNDS FOR ZEROS OF HOMOGENEOUS POLYNOMIAL SYSTEMS
Current Placement: The Museum of Mathematics, NYC

Advisor: Vaaler
Dissertation: THE STABILIZER OF THE GROUP DETERMINANT AND BOUNDS FOR LEHMER'S CONJECTURE OF FINITE ABELIAN GROUPS
Placement: Burapha University

Advisor: Knopf
Dissertation: ANALYSIS OF RICCI FLOW ON NONCOMPACT MANIFOLDS
Placement: Oregon

Advisor: Keel
Dissertation: A CRITERION FOR TORIC VARIETIES
Placement: CGG

Degree Awarded 2014

Advisor: Kui Ren
Dissertation: NUMERICAL ALGORITHMS FOR INVERSE PROBLEMS IN ACOUSTICS AND OPTICS
Placement: CGG

Advisor: Bjorn Engquist
Dissertation: NUMERICAL METHODS FOR MULTISCALE INVERSE PROBLEMS
Placement: Georgia Tech

Advisor: Jeffrey Vaaler
Dissertation: HEIGHTS AND INFINITE ALGEBRAIC EXTENSIONS OF THE RATIONALS
Placement: Wisconsin

Advisor: Sean Keel
Dissertation: THE FUNCTORIAL INTERPRETATION OF THE NAIVE COMPACTIFICATION OF REGULAR MORPHISM FROM PI1 TO PI1

Advisor: Jeffrey Vaaler
Dissertation: SOME INEQUALITIES IN FOURIER ANALYSIS AND APPLICATIONS
Placement: Michigan

Advisor: Mirela Ciperiani
Dissertation: SOME RESULTS IN IWASAWA THEORY AND THE P-ADIC REPRESENTATION THEORY OF P-ADIC GL2
Placement: Indiana

Advisor: Dr. Jonathan Pillow
Dissertation: RECOVERY OF CONTINUOUS QUANTITIES FROM DISCRETE AND BINARY DATA WITH APPLICATIONS TO NEURAL DATA
Placement: Phillips Academy, Andover, MA

Advisor: Dr. Cameron Gordon
Dissertation: SLICE RIBBON CONJECTURE, PRETZEL KNOTS AND MUTATION
Placement: CGG Veritas Inc.

Advisor: Sean Keel
Dissertation: TROPICAL THETA FUNCTIONS FOR LOG CALABI-YAU SURFACES
Placement: Aarhus University

Advisor: Cameron Gordon
Dissertation: EXCEPTIONAL SEIFERT FIBERED SURGERIES ON MONTESINOS KNOTS AND DISTINGUISHING SMOOTHLY AND TOPOLOGICALLY DOUBLY SLICE KNOTS
Placement: NSF postdoc: Indiana

Advisor: David Ben-Zvi
Dissertation: GEOMETRY OF INTEGRABLE HIERARCHIES AND THEIR DISPERSIONLESS LIMITS
Placement: Oxford

Advisor: Alan Reid
Dissertation: GEOMETRIC PROPERTIES OF OUTER AUTOMORPHISM GROUPS OF FREE GROUPS
Placement: NSF postdoc: Yale

Advisor: Natasa Pavlovic
Dissertation: FROM QUANTUM MANY BODY SYSTEMS TO NONLINEAR SCHROEDINGER EQUATIONS
Placement: University of Illinois at Chicago

Degree Awarded 2015

Advisor: Dr. Robert E Gompf
Dissertation: EXOTIC SMOOTHINGS VIA LARGE R4'S IN STEIN SURFACES
Placement: Netflix, Inc.

Advisor: Dr. Mikhail Vishik
Dissertation: ON THE LINEAR STABILITY PROBLEM FOR JEFFERY-HAMEL FLOWS

Advisor: Dr. Yen-Hsi (Richard) Tsai
Dissertation: IMPLICIT BOUNDARY INTEGRAL METHODS
Placement: Quantitative Analyst, Goldman Sachs

Advisor: Dr. Ronny Hadani
Dissertation: LABELING AND DENOISING GEOMETRICALLY PARAMETERIZED DATA WITH APPLICATIONS TO CRYO-EM

Advisor: Dr. Andrew Blumberg
Dissertation: THE ANDRE-QUILLEN SPECTRAL SEQUENCE FOR PRE-LOGARITHMIC RING SPECTRA

Advisor: Dr. Andrew Neitzke
Dissertation: A CONSTRUCTION OF HYPERKÄHLER METRICS THROUGH RIEMANN-HILBERT PROBLEMS
Placement: Indiana University Purdue University Indianapolis

Advisor: Dr. Rachel Ward
Dissertation: STRUCTURED LOW COMPLEXITY DATA MINING

Advisor: Dr. Mihai Sirbu
Dissertation: ASYMPTOTICS FOR OPTIMAL INVESTMENT WITH HIGH-WATER MARK FEE
Current Placement: Insight Data Science, Inc.

Advisor: Dr. Luis Caffarelli
Dissertation: A LOCAL-NONLOCAL TRANSMISSION PROBLEM
Placement: NSF Postdoc, Courant Institute of Mathematical Sciences

Advisor: Dr. Robert E Gompf
Dissertation: SOME CONSTRUCTIONS INVOLVING SURGERY ON SURFACES IN 4-MANIFOLDS
Placement: Postdoc Research Fellow, Renyi Institute, Budapest, Hungary

Advisor: Dr. Gordan Zitkovic
Dissertation: EXISTENCE, CHARACTERIZATION AND APPROXIMATION IN THE GENERALIZED MONOTONE FOLLOWER PROBLEM
Placement: Machine Learning Scientist, Amazon Inc.

Advisor: Dr. Daniel Allcock
Dissertation: THE CLASSIFICATION OF RANK 3 REFLECTIVE HYPERBOLIC LATTICES OVER Z [SQRT-(2)]
Placement: Arizona State University

Advisor: Dr. Jose F. Voloch
Dissertation: INTERPOLATING GAMMA FACTORS IN FAMILIES
Placement: Oklahoma State University

Advisor: Dr. David Ben-Zvi
Dissertation: COORDINATE SYSTEMS AND ASSOCIATIVE ALGEBRAS
Placement: Rabobank (Netherlands); Model Validator

Advisor: Dr. Todd Arbogast
Dissertation: A QUADRATURE EULERIAN-LAGRANGIAN WENO SCHEME FOR RESERVOIR SIMULATION
Placement: University of Texas at Austin

Advisor: Dr. Robert Gompf
Dissertation: CLASSIFICATIONS AND APPLICATIONS OF SYMPLECTIC FILLINGS OF SEIFERT FIBERED SPACES OVER S^2
Placement: NSF Postdoc Stanford University

Advisor: Dr. Thomas Chen
Dissertation: THE DYNAMICS OF BOSE GASES
Current Placement: Insight Data Science, Inc.

Advisor: Dr. Kui Ren
Dissertation: QUANTITATIVE PAT WITH UNKNOWN ULTRASOUND SPEED: UNCERTAINTY CHARACTERIZATION AND RECONSTRUCTION METHODS
Placement: SAMSI / North Carolina State University

Advisor: Dr. Rachel Ward
Dissertation:
Placement: Principle Quantitative Analyst, Capital One Banking

Advisor: Dr. Sean Keel
Dissertation: COMPACTIFICATION OF MODULI SPACES AND MIRROR SYMMETRY
Placement: University of Pennsylvania

Advisor: Dr. Cameron Gordon
Dissertation: THE COMBINATORICS OF REDUCIBLE DEHN SURGERIES
Placement: Imperial College

Degree Awarded 2016

Advisor: Dr. Felipe Voloch
Dissertation: OBSTRUCTIONS TO THE INTEGRAL HASSE PRINCIPLE FOR GENERALIZED AFFINE CHATELET SURFACES
Placement: Rice University, RTG Lovett Instructor

Advisor: Dr. Dan Freed
Dissertation: Rectifying Stable Infinity-Categories and Relative Koszul Duality for Operads
Placement: Data Scientist, In-Q-Tel, Washington, DC

Advisor: Dr. Andrew Neitzke
Dissertation: WARPING GEOMETRIC STRUCTURES AND ABELIANIZING SL2R LOCAL SYSTEMS
Placement: University of Toronto, Postdoctoral Fellow

Advisor: Dr. Andrew Neitzke
Dissertation: ASYMPTOTIC LIMITS IN THE HITCHIN MODULI SPACE
Placement: Stanford University, Szego Visiting Assistant Professor

Advisor: Dr. Ronny Hadani
Dissertation: EXPLORATIONS IN ALGEBRA AND TOPOLOGY
Placement: Center for Transportation Research, University of Texas at Austin

Advisor: Dr. David Ben-Zvi
Dissertation: THE WONDERFUL COMPACTIFICATION FOR QUANTUM GROUPS
Placement: Institute of Science and Technology Austria, Postdoctoral Researcher

Advisor: Dr. Gordan Zitkovic
Dissertation: RECOVERING THE PAYOFF STRUCTURE OF A UTILITY MAXIMIZING AGENT

Advisor: Dr. Mirela Ciperiani
Dissertation: MULTIPLICATIVE AND DYNAMICAL ANALYSIS ON IDELES AND IDELE CLASS GROUPS

Advisor: Dr. Luis Caffarelli
Dissertation: REGULARITY ESTIMATES FOR SOME FREE BOUNDARY PROBLEMS OF OBSTACLE-TYPE
Placement: McGill University, Postdoctoral Fellow

Advisor: Dr. Andrew Blumberg
Dissertation: ASPECTS OF DERIVED KOSZUL DUALITY
Placement: University of California Los Angeles, NSF Postdoctoral Fellow

Advisor: Dr. Lewis Bowen
Dissertation: Entropy theory for locally compact sofic groups
Placement: Associate, Model Risk, Internal Audit, Goldman Sachs NYC

Advisor: Dr. Irene Gamba
Dissertation: MITTAG-LEFFLER MOMENTS AND WEIGHTED POINTWISE ESTIMATES FOR SOLUTIONS TO THE BOLTZMANN EQUATION FOR HARD POTENTIALS WITHOUT CUTOFF
Placement: University of Pennsylvania, Hans Rademacher Instructor of Mathematics

Degree Awarded 2017

Advisor: Dr. Irene Gamba
Dissertation: Global LP Solutions to the Boltzmann Equation with an Angle-Potential Concentrated Collision Kernel
Placement: Prager Assistant Professor of Applied Mathematics, Brown University

Advisor: Dr. Dan Freed
Dissertation: Rectifying Stable Infinity-Categories and Relative Koszul Duality for Operads
Placement: Data Scientist, In-Q-Tel, Washington, DC

Advisor: Dr. Raymond Heitmann
Dissertation: Cardinality Restrictions on Noetherian Spectra
Placement: Gaius Charles Bolin Research Fellow in Mathematics, Williams College

Advisor: Dr. Lewis Bowen, Dr. Amir Mohammadi
Dissertation: Effective Equidistribution Results for Horospherical Actions on the Space of Lattices
Placement: Lecturer, University of Texas at Austin

Advisor: Dr. Gordan Zitkovic
Dissertation: Martingale-Generated Control Structures and a Framework for the Dynamic Programming Principle
Placement: Data Scientist, Spark Cognition, Inc.

Advisor: Dr. Andrew Blumberg
Dissertation: A Weighty Theorem of the Heart for the Algebraic K-Theory of Higher Categories
Placement: Ross Assistant Professor, Ohio State

Advisor: Dr. Thaleia Zariphopoulou
Dissertation: Essays on Forward Portfolio Theory and Financial Time Series Modeling
Placement: Consultant, The Boston Consulting Group (BCG)

Advisor: Dr. Timothy Perutz
Dissertation: Lagrangian Torus Fibrations for Symplectic Torid Degenerations
Placement: Simons Postdoctoral Fellow, University of Pennsylvania

Advisor: Dr. Philip Uri Treisman
Dissertation: Academic Math Mindset Interventions in First Year College Calculus
Placement: Lecturer, University of Texas at Austin

Advisor: Dr. Timothy Perutz
Dissertation: Mapping Tori and Stable Pairs
Placement: Postdoctoral Scholar, University of California Santa Cruz

Advisor: Dr. Mihai Sirbu
Dissertation: Optimal Investment with High-Watermark Fee in a Multi-dimensional Jump Diffusion Model
Placement: Associate, Goldman Sachs NYC

Advisor: Dr. Sean Keel
Dissertation: GHK Mirror Symmetry and the Knutson-Tao Hive Cone
Placement: Postdoctoral Fellow, Instituto de Matematicas Unidad Oaxaca, Mexico

Advisor: Dr. Luis Caffarelli
Dissertation: Least Action Principles with Applications to Gradient Flows and Kinetic Equations
Placement: Postdoctoral Fellow, University of Maryland, College Park

Advisor: Dr. Francesco Maggi, Dr. Allesio Figalli
Dissertation: Minimality and Stability Properties in Sobolev and Isoperimetric Inequalities
Placement: RTG Postdoctoral Fellow, Northwestern University

Advisor: Dr. Felipe Voloch
Dissertation: Differential FPPF Descent Obstructions
Placement: TA Specialist, University of Texas at Austin

Advisor: Dr. Rachel Ward
Dissertation: Relax, Descend, and Certify: Optimization Techniques for Typically Tractable Data Problems
Placement: Moore-Sloan Research Fellow, New York University, Center for Data Science

Advisor: Dr. Luis Caffarelli
Dissertation: Several Regularity Results for Nonlocal Elliptic Equations
Placement: Ritt Assistant Professor, Columbia University

Advisor: Dr. Kui Ren
Dissertation: Hybrid Inverse Problems in Molecular Imaging
Placement: Applied Scientist, Amazon

Advisor: Dr. Kui Ren
Dissertation: Inverse Problems in Photoacoustic Imaging: Analysis and Computation
Placement: Postdoctoral Fellow, University of California, Irvine