## Mathematics Alumni

### Degree Awarded 2023

Advisor: David Ben-Zvi

Dissertation: Chromatic applications of spectral algebraic geometry

Placement: Johns Hopkins University

Advisor: Luis Caffarelli & Francesco Maggi

Dissertation: The Allen-Cahn Euclidean isoperimetric problem and
the Grad-Mercier equation in Plasma physics

Placement: Johns Hopkins University

### Degree Awarded 2022

Advisor: Irene Gamba

Dissertation: COERCIVENESS, WELL-POSEDNESS, AND BANACH NORMS PROPAGATION OF SOLUTIONS TO THE SYSTEM OF BOLTZMANN EQUATIONS FOR A MONATOMIC GAS MIXTURE

Placement: Algorithm Developer - Trace

Advisor: Samuel Raskin

Dissertation: CATEGORICAL REPRESENTATION THEORY AND THE COARSE QUOTIENT

Placement: UCLA

Advisor: Rachel Ward

Dissertation: TENSOR DIMENSIONALITY REDUCTION AND APPLICATIONS

Placement: University of Wisconsin-Madison

Advisor: Cameron Gordon

Dissertation: SYMMETRIC UNION OF KNOTS, DOUBLE BRANCHED COVERS AND DEHN SURGERY

Placement: University of Georgia

Advisor: Philip Isett & Alexis F Vasseur

Dissertation: SOME ONSAGER'S CONJECTURE TYPE RESULTS FOR A FAMILY OF ODD ACTIVE SCALAR EQUATIONS

Advisor: David Ben-Zvi & Andrew Neitzke

Dissertation: NILPOTENT HIGGS BUNDLES AND FAMILIES OF FLAT CONNECTIONS

Placement: MSRI & Johns Hopkins University

Advisor: Luis Caffarelli & Pablo Raul Stinga

Dissertation: REGULARITY OF ELLIPTIC TRANSMISSION PROBLEMS AND A NEW FAMILY OF INTEGRO-DIERENTIAL OPERATORS RELATED TO THE MONGE-AMPERE EQUATION

Placement: Rutgers University

Advisor: Luis Caffarelli & Francesco Maggi

Dissertation: FULLY NONLINEAR EQUATIONS WITH APPLICATIONS TO GRAD EQUATIONS IN PLASMA PHYSICS. INTERACTION BETWEEN A ONE PHASE FREE BOUNDARY PROBLEM AND AN OBSTACLE PROBLEM. OPTIMAL TRACE SOBOLEV INEQUALITIES

Advisor: Jeff Danciger

Dissertation: HIGHER-RANK GENERALIZATIONS OF CONVEX COCOMPACT AND GEOMETRICALLY FINITE DYNAMICS

Placement: University of Michigan

Advisor: Omar Ghattas & J T Oden

Dissertation: OPTIMAL EXPERIMENTAL DESIGN FOR LARGE-SCALE BAYESIAN INVERSE PROBLEMS

Placement: Research Scientist - Meta

Advisor: Omar Ghattas & J T Oden

Dissertation: OPTIMAL EXPERIMENTAL DESIGN FOR LARGE-SCALE BAYESIAN INVERSE PROBLEMS

Placement: University of Miami

Advisor: Luis Caffarelli & Alexis Vasseur

Dissertation: PARTIAL REGULARITY RESULTS FOR THE THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATION

Placement: University of Chicago

### Degree Awarded 2021

Advisor: Thomas Chen

Dissertation: ON THE DERIVATION AND UNIQUENESS OF THE GROSS-PITAEVSKII HIERARCHY FOR A BOSE GAS COUPLED TO A HEAVY TRACER PARTICLE

Placement: MS Quantum Information Science - University of Southern California

Advisor: David Ben-Zvi & Andrew Blumberg

Dissertation: A CONVENIENT CATEGORY FOR GEOMETRIC TOPOLOGY

Advisor: Daniel Freed

Dissertation: TAKING TOPOLOGICAL FIELD THEORY AT PHASE VALUE

Placement: Postdoc - Purdue University

Advisor: Arie Israel

Dissertation: APPROXIMATE EXTENSION IN SOBOLEV SPACE

Placement: NSF Postdoctoral Fellow - University of Pittsburgh & MIT (+ Moore Instructorship)

Advisor: Arie Israel

Dissertation: APPROXIMATE EXTENSION IN SOBOLEV SPACE

Placement: NSF Postdoc - University of Pittsburgh & MIT (+ Moore Instructorship)

Advisor: David Ben-Zvi & Andrew Blumberg

Dissertation: GEOMETRIC DATA ANALYSIS FOR PHYLOGENETIC TREES AND NON-CONTRACTIBLE MANIFOLDS

Placement: Postdoc - Oxford University

Advisor: Cameron Gordon

Dissertation: TWO-BRIDGE LINKS, PRETZEL KNOTS AND BI-ORDERABILITY

Placement: Postdoc - Oklahoma State University

Advisor: Francesco Maggi

Dissertation: A CAPILLARITY MODEL FOR SOAP FILMS

Placement: NSF postdoc at Courant Institute - New York University

Advisor: Jeffrey Danciger

Dissertation: A LOCAL-TO-GLOBAL PRINCIPLE FOR MORSE QUASIGEODESICS

Placement: Postdoc - University Heidelberg

Advisor: Irene Gamba

Dissertation: THE LANDAU LIMIT OF THE BOLTZMANN EQUATION AND FAST PARTICLE MOTION IN A TOKAMAK

Placement: Assistant Professor of Instruction - The University of Texas at Austin

Advisor: Cameron Gordon

Dissertation: SYMMETRIES OF KNOTS, BRANCHED CYCLIC COVERS, AND L-SPACES

Placement: Postdoc - Georgia Tech

Advisor: Thomas Chen

Dissertation: NONLINEAR SCHRODINGER SYSTEMS ON THE THREE-DIMENSIONAL TORUS

Placement: Senior Professional Staff - Johns Hopkins University - Applied Physics Lab

Advisor: David Ben-Zvi & Andrew Blumberg

Dissertation: ENDO-TRIVIAL MODULES FOR CYCLIC P-GROUPS AND GENERALIZED QUATERNION GROUPS VIA GALOIS DESCENT

Placement: Assistant Adjunct Professor University of California, Los Angeles

Advisor: Thomas Chen

Dissertation: ON THE WEAKLY DISORDERED ANDERSON MODEL AND ASPECTS OF ITS KINETIC SCALING LIMIT TO THE LINEAR BOLTZMANN EQUATION

### Degree Awarded 2020

Advisor: Natasa Pavlovic

Dissertation: Higher order extensions of the Boltzmann equation

Placement: New York University

Advisor: Jeffrey Danciger

Dissertation: Cusps and Codimension-1 Flats in Convex Projective Geometrey

Placement: University of Michigan

Advisor: Björn Engquist

Dissertation: Numerical Multiscale Methods for Boundary Layer Problems in Fluid Dynamics

Placement: University of California, Los Angeles

Advisor: Francois Baccelli

Dissertation: On Poisson Follower Model

Placement: Tufts University

Advisor: Bjorn Engquist

Dissertation: Numerical Methods for Averaging and Homogenization

Advisor: Arie Israel

Dissertation: Coordinate-Free Principles for Extension of Smooth Functions

Placement: Striveworks

Advisor: Alexis Vasseur

Dissertation: The L2 Theory of Well-posedness for Hyperbolic Systems of Conservation Laws

Placement: Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany

Advisor: Sean Keel

Dissertation: Compactified Mirror Families for Positive Log Calabi-Yau Surfaces

Placement: Imperial College

Advisor: Lewis Bowen

Dissertation: Non-unique sofic entropy and a von Neumann algebra multiplicative ergodic theorem

Placement: Ben Gurion University of the Negev

Advisor: Thibaud O Taillefumier

Dissertation: OPTIMIZING MUTUAL INFORMATION OVER NEURAL TUNING CURVES

Placement: AI Data Scientist - Change Healthcare

Advisor: Irene M. Gamba

Dissertation: Conservative Spectral Methods of Fokker-Planck-Landau Type Equations: Simulations, Long-time Behaviour and Error Estimates

Placement: Trace

Advisor: Natasa Pavlovic

Dissertation: Old and New Perspectives on Effective Equations: A Study of Quantum Many-Body Systems

Placement: Massachusetts Institute of Technology

Advisor: Alexis Vasseur

Dissertation: The De Giorgi method: Applications to degenerate PDE

Placement: Fields Institute

Advisor: Daniel Freed and Andrew Neitzke

Dissertation: The Ooguri-Vafa as a moduli space of framed wild harmonic bundles

Placement: University of Hamburg

Advisor: Rachel Ward and Leon Bottou

Dissertation: GRADIENT-BASED OPTIMIZATION AND IMPLICIT REGULARIZATION OVER NON-CONVE X LANDSCAPES

Placement: Postdoc - University of Chicago

### Degree Awarded 2019

Advisor: Arie Israel

Dissertation: Extremal problems in Fourier analysis, Whitney's theorem, and the interpolation of data

Placement: Princeton University

Advisor: Andrew Blumberg

Dissertation: Andre-Quillen (co)homology and equivariant stable homotopy theory

Advisor: Francois Baccelli

Dissertation: On Spatial Birth-Death and Matching Processes, and Poisson Shot-Noise Fields

Placement: Enthought Inc.

Advisor: Yen-Hsi Tsai

Dissertation: Methods for Solving Hamilton-Jacobi-Equations

Placement: The Boeing Company

Advisor: Francois Baccelli

Dissertation: Coupling and Unimodularity in Stationary Settings

Placement: Chicago Trading Company

Advisor: Alexis Vasseur

Dissertation: A Study of the Three-Dimensional Quasi-Geostrophic System

Placement: New York University

Advisor: Francois Baccelli

Dissertation: Repulsion of Determinantal Point Processes and Stationary Poisson Tessellations in High Dimesions

Placement: California Institute of Technology

Advisor: Sean Keel

Dissertation: On the dual complexes of certain Log Calabi-Yau pairs

Placement: Meridian World School

Advisor: John Luecke

Dissertation: Knot traces and the slice genus

Placement: Massachusetts Institute of Technology

Advisor: Andrew Blumberg

Dissertation: The moduli space of objects in differential graded categories glued along bimodules & a presentability result in the homotopy theory of commutative differential graded algebras

Placement: University of Texas at Austin

Advisor: Daniel Knopf

Dissertation: Curvature Blow-up in Doublywarped Product Metrics Evolving by Ricci Flow

Placement: Arizona State University

Advisor: Andrew Blumberg

Dissertation: Equivariant aspects of topological Hochschild homology

Placement: Brown University

Advisor: Luis A. Caffarelli

Dissertation: Regularity of fractional analogue of k-Hessian operators and a non-local one-phase free boundary problem

Placement: University of Maryland, College Park

Advisor: Andrew Blumberg

Dissertation: Comparison Theorems of Phylogenetic Spaces and Algebraic Fans

Placement: Harvard University

Advisor: Sean Keel

Dissertation: Admissible groups and cluster structures of families of log Calabi-Yau surfaces

### Degree Awarded 2018

Advisor: Rachel Ward

Dissertation: Fast high dimensional approximation via random embeddings

Placement: Gilliam IP PLLC

### 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

### 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 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 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 2013

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

### Degree Awarded 2012

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: Caffarelli

Dissertation:

Placement: Univ. of British Columbia

Advisor: Vishik

Dissertation: INCOMPRESSIBLE BOUSSINESQ EQUATIONS AND SPACES OF BORDERLINE BESOV TYPE

Placement: Lockheed Martin Corp.

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: 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 2011

Advisor: Radin

Dissertation: ORDERING IN DENSE PACKINGS

Placement: Univ. of Minnesota

Advisor: De La Llave

Dissertation: ON THE AUBRY-MATHER THEORY FOR PARTIAL DIFFERENTIAL EQUATIONS AND THE STABILITY OF STOCHASTICALY FORCED ORDINARY DIFFERENTIAL EQUATIONS

Placement: Carnegie-Mellon

Advisor: Beckner/Pavlovic

Dissertation: GLOBAL WELL-POSEDNESS AND SCATTERING FOR THE DEFOCUSING ENERGY- SUPERCRITICAL CUBIC NONLINEAR WAVE EQUATION

Placement: Princeton Institute for Advanced Study

Advisor: Freed

Dissertation: STATE SUMS IN TWO DIMENSIONAL FULLY EXTENDED TOPOLOGICAL FIELD THEORIES

Current Placement: Northwestern University

Advisor: Bajaj

Dissertation: STABILITY OF DUAL DISCRETIZATION METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS

Placement: Univ. of Calif. at San Diego

Advisor: Gordon

Dissertation: PRIMITIVE/PRIMITIVE AND PRIMITIVE/SEIFERT KNOTS

Placement: Univ. of Texas, Austin

Advisor: Reid

Dissertation: PROPERTIES OF COMMENSURABILITY CLASSES OF HYPERBOLIC KNOT COMPLEMENTS

Placement: Boston College

Advisor: Reid

Dissertation: ON THE CANONICAL COMPONENTS OF CHARACTER VARIETIES OF HYPERBOLIC 2-BRIDGE LINK COMPLEMENTS

Placement: Technion-Israel Institute of Technology

Advisor: Vaaler

Dissertation: NORMS EXTREMAL WITH RESPECT TO THE MAHLER MEASURE AND A GENERALIZATION OF DIRICHLET'S UNIT THEOREM

Placement: Univ. of Texas, Austin

Advisor: Zariphopolou

Dissertation: Three Essays on Valuation and Investment in Incomplete Markets

Placement: Susquehanna International Group--Philadelphia, PA

Advisor: Voloch

Dissertation: THE INTERSECTION OF CLOSURE OF GLOBAL POINTS OF A SEMI-ABELIAN VARIETY WITH A PRODUCT OF LOCAL POINTS OF ITS SUBVARIETIES

Placement: Academia Sinica, Taiwan

Advisor: Caffarelli

Dissertation: RANDOM HOMOGENIZATION OF P-LAPLACIAN WITH OBSTACLES ON PERFORATED DOMAIN AND RELATED TOPICS

Placement: Univ. of Iowa

Advisor: Dan Knopf

Dissertation: ANALYSIS OF GEOMETRIC FLOWS, WITH APPLICATIONS TO OPTIMAL HOMOGENEOUS GEOMETRIES

Placement: UCLA

Advisor: Caffarelli

Dissertation: OPTIMAL REGULARITY AND NONDEGENERACY FOR MINIMIZERS OF AN ENERGY RELATED TO THE FRACTIONAL LAPLACIAN

Placement: Courant Institute of Mathematical Sciences

### Degree Awarded 2010

Advisor: Rodriguez-Villegas

Dissertation: ON REAL AND P-ADIC BEZOUTIANS

Current Placement: Universidad Nacional de Moreno

Advisor: Vaaler

Dissertation: ORTHOGONAL DECOMPOSITIONS OF THE SPACE OF ALGEBRAIC NUMBERS MODULO TOR

Placement: University of Rochester

Advisor: Caffarelli

Dissertation: REGULARIZATION IN PHASE TRANSITIONS WITH GIBBS-THOMSON LAW

Current Placement: UCLA

Advisor: Rodriguez-Villegas

Dissertation: PERIODS OF MODULAR FORMS AND CENTRAL VALUES OF L-FUNCTIONS

Current Placement: Director-R &D Tax Credits

Advisor: Keel

Dissertation: BIRATIONAL GEOMETRY OF THE MODULI SPACES OF CURVES WITH ONE MARKED POI

Placement: Stony Brook University

Advisor: Sadun

Dissertation: ROTATIONAL COHOMOLOGY AND TOTAL PATTERN EQUIVARIANT COHOMOLOGY OF TILING

Current Placement: Huston-Tillotson University

Advisor: Reid

Dissertation: ON SOME RESIDUAL AND LOCALLY VIRTUAL PROPERTIES OF GROUPS

Placement: Software Engineer at Hurricane Inc.

Advisor: Vasseur

Dissertation: A FRAGMENTATION MODEL FOR SPRAYS AND L2 STABILITY ESTIMATES FOR SHOCKS

Placement: Carnegie-Mellon University

Advisor: Ben-Zvi

Dissertation: AUTOEQUIVALENCES, STABILITY CONDITIONS, AND N-GONS

Placement: Western Ontario University

Advisor: Rodriguez-Villegas

Dissertation: ON THE E-POLYNOMIALS OF A FAMILY OF CHARACTER VARIETIES

Placement: Oxford University

Advisor: Ben-Zvi

Dissertation: SHEAF THEORETIC METHODS IN MODULAR REPRESENTATION THEORY

Placement: Harvard University

Advisor: Saltman

Dissertation: RATIONAL EMBEDDINGS OF THE SEVERI-BRAUER VARIETY

Placement: University of Texas at Austin

Advisor: Caffarelli

Dissertation: ABOUT THE LARGEST SUBSOLUTION FOR A FREE BOUNDARY PROBLEM IN R2: ELLIP

Current Placement: Rice University

Advisor: Allcock

Dissertation: FIXED-POINT-FREE ACTIONS OF COXETER GROUPS ON THREE-DIMENSIONAL CAT(0)

Placement: University of Arizona

Advisor: Rodriguez-Villegas

Dissertation: THE DISTRIBUTION OF ROOTS OF CERTAIN POLYNOMIALS

Advisor: Vaaler

Dissertation: AN ANALOGUE OF THE KORKIN-ZOLOTAREV LATTICE REDUCTION FOR VECTOR SPACES OVER NUMBER FIELDS

Advisor: Ying

Dissertation: FAST DIRECT ALGORITHMS FOR ELLIPTIC EQUATIONS VIA HIERARCHICAL MATRIX COMPRESSION

Advisor: Reid

Dissertation: CUSPS OF HERMITIAN LOCALLY SYMMETRIC SPACES

Placement: University of Michigan

Advisor: Odell

Dissertation: ON S1-STRICTLY SINGULAR OPERATORS

Placement: Univ. of Houston-Victoria

Advisor: Gompf

Dissertation: BROKEN LEFSCHETZ FIBRATIONS ON SMOOTH FOUR-MANIFOLDS

Placement: Univ. of California-Berkeley

### Degree Awarded 2009

Advisor: Fernando Rodriguez Villegas

Dissertation: L-Functions of Elliptic Curves over Function Fields

Placement: University of Washington

Advisor: Felipe Voloch

Dissertation: Characterization of Multi-Frobenius Non-Classical Plane Curves and construction of complete Plane (N,D)-ARCS

Placement: University of Sao Paulo, Sao Carlos Campus

Advisor: Alan Reid

Dissertation: The Arithmetic and Geometry of Two-Generator Kleinian Groups

Placement: St. Edward's University

Advisor: Rafael de la Llave

Dissertation: Existence and persistence of invariant objects in dynamical systems and mathematics physics

Placement: McGill University

Advisor: William Beckner and Jeff Vaaler

Dissertation: Extremality, Symmetry and Regularity Issues in Harmonic Analysis

Placement: Institute for Advanced Study, Princeton University

Advisor: Felipe Voloch

Dissertation: Generalizing Binary Quadratic Residue Codes to higher power Residues over larger fields

Placement: Federal Government

Advisor: Felipe Voloch

Dissertation: Twists of Elliptic Curves with a larger set of integral points over (FQ(T)

Placement: Oxford College of Emory University

Advisor: Gordan Zitkovic

Dissertation: The Optimal Control of a Levy Process

Placement: Bloomberg L.P.

Advisor: Fernando Rodriguez-Villegas

Dissertation: Computing the Tutte Polynomial of Hyperplane Arrangements

Placement: Applied Research Laboratories

Advisor: Vaaler

Dissertation: On some distribution problems in Analytic
Number Theory

Placement: Yahoo Japan Corporation

Advisor: Cameron Gordon

Dissertation: Reducible and Toroidal Dehn Fillings with Distance 3

Placement: Boston College

Advisor: Daniel Freed

Dissertation: Differential Equivariant K-theory

Placement: Sul Ross State University

Advisor: Sean Keel

Dissertation: Toric Schemes over a discrete Valuation Ring and Tropical Compactifications

Placement: East China Normal University

Advisor: Fernando Rodriguez-Villegas

Dissertation: Hypergeometric Functions in Arithmetic Geometry

Placement: Bates College

Advisor: Panagiotis Souganidis/Luis Caffarelli

Dissertation: Random and Periodic Homogenization for some Nonlinear Partial Differential Equations

Placement: Carnegie Mellon University

Advisor: Tandy Warnow

Dissertation: Phylogenetic Supertree Methods

Placement: University of Texas at Austin

Advisor: Mikhail Vishik

Dissertation: Linear Instability for Incompressible inviscid fluid flows: two classes of perturbations

Placement: University of California Santa Barbara

### Degree Awarded 2008

Advisor: Irene Gamba

Dissertation: The Boltzmann Equation: Sharp Povzner Inequalities applied to regularity theory

Placement: Visiting Professor, Brown University

Advisor: Gordan Zitkovic

Dissertation: Agents' Agreement and Partial Equilibrium Pricing in Incomplete Markets

Placement: Athens, Greece

Advisor: Alexis Vasseur

Dissertation: The De Giorgi's Method as Applied to the Regularity Theory of Incompressible Navier Stokes equations

Placement: University of Minnesota

Advisor: Karen Uhlenbeck

Dissertation: Well-Posedness for the Space-Time Monopole Equation and Ward Wave Map

Placement: University of Toronto

Advisor: Jeffrey Vaaler

Dissertation: The Height in Terms of the Normalizer of a Stabilizer

Placement: Kansas State University

Advisor: David Saltman

Dissertation: Regular Realizations of P-Groups

Placement: University of Texas at Austin

Advisor: Daniel Freed

Dissertation: Superconnections and Index Theory

Placement: Goettingen University, Germany

Advisor: Daniel Freed

Dissertation: An Index Theorem in Differential K-Theory

Placement: Constellation Energy

Advisor: Sean Keel

Dissertation: The Log Canonical Compactification of the Moduli of Six Lines in P^2

Advisor: David Saltman

Dissertation: The Discriminant Algebra in Cohomology

Placement: S D & M Software, Munich, Germany

Advisor: Daniel Freed

Dissertation: Abelian Chern-Simons Theory with Toral Gauge Group, Modular Tensor Categories, and Group Categories

Placement: Postdoctoral Researcher, University of Utah

Advisor: Karen Uhlenbeck

Dissertation: Modified Ricci Flow on a Principal Bundle

Placement: University of Arizona

Advisor: Thaleia Zariphopoulou

Dissertation: Essays on Pricing and Portfolio Choice in Incomplete Markets

### Degree Awarded 2007

Advisor: Panagiotis Souganidis

Dissertation: Singular Limits of Reaction Diffusion Equations of KPP type in an infinite Cylinder

Placement: Visiting Professor, Arizona State University

Advisor: Mikhail Vishik

Dissertation: Incompressible Fluids with Vorticity in Besov Spaces

Placement: Postdoctoral Associate, Carnegie Mellon University

Advisor: Alan Reid

Dissertation: Totally Geodesic Surfaces in Hyperbolic 3-Manifolds

Current Placement: University of Illinois at Chicago

Advisor: Karen Uhlenbeck

Dissertation: The Higher Flows of Harmonic Maps

Current Placement: Jacksonville University

Advisor: Felipe Voloch

Dissertation: Incompleteness of the Glalietti-Ughi Arc

Placement: Quantitative Risk Control, UBS, New York, NY

Advisor: Felipe Voloch

Dissertation: Genus 2 Curves in pairing-based Cryptography and the minimal embedding field

Current Placement: 21st Century Technologies, Austin

Advisor: Alexis Vasseur

Dissertation: Strong Trace for Degenerate Parabolic-Hyperbolic Equations and Applications

Current Placement: University of Maryland at College Park

Advisor: Luis A. Caffarelli

Dissertation: Least Supersolution Approach to regularizing Elliptic Free Boundary Problems

Placement: Visiting Assistant Professor, University of Iowa

Advisor: Jeffrey D. Vaaler

Dissertation: Auxiliary Polynomials and Height Functions

Current Placement: Univ. of British Columbia, Vancouver

Advisor: Todd Arbogast

Dissertation: A Three-Dimensional Finite Element Method and Multigrid Solver for a Darcy-Stokes System and Applications to Vuggy Porous Media

Placement: State University of New York at Buffalo

Advisor: Robert E. Gompf

Dissertation: Constructions on Open Book Decompositions

Placement: Postdoctoral Fellow, University of Quebec at Montreal

### Degree Awarded 2006

Advisor: Alan Reid

Dissertation: Undetected Boundary Slopes and Roots of unity for the character variety of a Three-Manifold

Placement: Evans Instructor, Rice University

Advisor: Cameron Gordon

Dissertation: Heegaard Splittings of Toroidal Three-Manifolds

Placement: Assistant Professor, American University in Cairo, Egypt

Advisor: Rafael de la Llave

Dissertation: Renormalization and Central Limit Theorem for Critical Dynamical Systems with external weak random noise

Current Placement: Precision Health Economics, Austin TX

Advisor: Panagiotis Souganidis

Dissertation: Forced Vibrations via Nash-Moser Iterations

Placement: Post-Doctoral Fellow, McMaster University, Ontario, Canada

Advisor: Jeff Vaaler

Dissertation: Tools and Techniques in Diophantine Approximation

Placement: Lecturer, Mathematics, The University of Texas at Austin

Advisor: Jose Felipe Voloch

Dissertation: On the suitability of power functions as S-boxes for symmetric cryptosystems

Placement: Research Mathematician, United States Department of Defense

Advisor: Uri Treisman

Dissertation: Factors in statistics learning: Developing a dispositional attribution model to describe the development of statistical proficiency

Placement: Assistant Professor, Michigan State University

Advisor: Cameron Gordon

Dissertation: Geometry and Algebra of Hyperbolic 3-Manifolds

Placement: Tamarkin Assistant Professor and National Science Foundation Post-Doctoral Fellow, Brown University

Advisor: Alan Reid

Dissertation: Derived Arithmetic Fuchsian Groups of Genus Two

Placement: Post-Doctoral Fellow, University of British Columbia

Advisor: David Saltman

Dissertation: Non-cyclic and Indecomposable P-algebras

Placement: : National Science Foundation Mathematical Sciences Post-Doctoral Fellowship, Emory University/Rice University

Advisor: Alan Reid

Dissertation: Cusps of Arithmetic Orbifolds

Placement: Olga Taussey-John Todd Instructor, California Institute of Technology

Advisor: Jack Xin

Dissertation: Reaction-Diffusion Fronts in Inhomogeneous Media

Placement: National Science Foundation Postdoctoral Scholar, Stanford University

Advisor: Jeff Vaaler

Dissertation: Diophantine approximation in projective space and the absolute Siegelâ€™s Lemma

Placement: Actuarial Analyst, Mercer Human Resource Consulting, Los Angeles, California

Advisor: Lorenzo Sadun

Dissertation: Pattern-Equivariant Chomology of Tiling Spaces with Rotations

Placement: Assistant Professor, Texas Lutheran University

Advisor: Dan Freed

Dissertation: Local Elliptic Boundary Value Problems for the Dirac Operator

Placement: Lecturer, The University of Texas at Austin

Advisor: Jose Felipe Voloch

Dissertation: Error-Correcting Codes on low Neron-Severi rank surfaces

Placement: Assistant Professor, Emory and Henry College, Emory, Virginia

### Degree Awarded 2005

Advisor: Todd Arbogast

Dissertation: Simulating Fluid Flow in Vuggy Porous

Advisor: Mikhail Vishik

Dissertation: The vanishing Viscosity Limit for Incompressible Fluids in two dimensions

Placement: Tamarkin Assistant Professor, Brown University

Advisor: Fernando Rodriguez-Villegas

Dissertation: Some relations of Mahler measure with hyperbolic volumes and special values of L-Functions

Current Placement: Associate Professor, Universite de Montreal, Canada

Advisor: Jack Xin

Dissertation: Human Acoustics: From Vocal Chords to Inner Ear

Placement: Postdoctoral Associate, Cornell University

Advisor: Fernando Rodriguez-Villegas

Dissertation: Some applications of classical modular forms to number theory

Placement: Postdoctoral Fellow, Max Planck Institute for Mathematics,

Advisor: Sean Keel

Dissertation: An Elementary Construction of M0,0

Placement: Assistant Professor, Wittenberg University, Springfield, Ohio

Advisor: Alan Reid

Dissertation: One-Cusped Congruence Subgroups of PSL2

Placement: Coleman Postdoctoral Fellow, Queen's University, Ontario, Canada

Advisor: Luis Caffarelli

Dissertation: Regularity of the obstacle problem for a fractional power of the Laplace Operator

Placement: Postdoctoral Instructor, Courant Institute, New York, New York

Advisor: Jeffrey Vaaler

Dissertation: Multiplicative Distance Functions

Current Placement: Univ. of Oregon

Advisor: Thaleia Zariphopoulou

Dissertation: Optimal Strategies in incomplete financial markets

Placement: Postdoctoral Instructor, Courant Institute, New York, New York

Advisor: Luis Caffarelli

Dissertation: Regularity of Free Boundary in variational problems

Placement: Postdoctoral Assistant Professor, State University of New Jersey at Rutgers

Advisor: Fernando Rodriguez-Villegas

Dissertation: The Brandt Module of Ternary Quadratic Lattices

Current Placement: Profesor Adjunto, Universidad de la República, Uruguay

### Degree Awarded 2004

Advisor: John Luecke

Dissertation: Knots on Once-punctured Torus Fibers

Placement: VIGRE, University of Georgia at Athens

Advisor: Fernando Rodriguez Villegas

Dissertation: Mahler Measure Evaluations in terms of Polylogarithms

Placement: Visiting Assistant Professor, City University of New York

Advisor: Jeffrey Vaaler

Dissertation: Algebraic Points of Small Height with Additional Arithmetic Conditions

Placement: Visiting Assistant Professor, Texas A & M University

Advisor: Todd Arbogast

Dissertation: Analysis of a Darcy-Stokes System Modeling Fluid Flow in Vuggy Porous Media

Placement: Ohio State University

Advisor: Jeff Vaaler

Dissertation: Distribution of Galois Orbits of Low Height

Placement: VIGRE Post Doctoral Associate, University of Georgia at Athens

Advisor: Felipe Voloch

Dissertation: Computations on an Equation of the BSD Type

Placement: Universidad Nacional Autonoma de Mexico

### Degree Awarded 2003

Advisor: Robert Gompf

Dissertation: Contact Structures and Open Books

Current Placement: Post Doctoral Appointment, Massachusetts Institute of Technology

Advisor: Karen Uhlenbeck

Dissertation: Adiabatic Limits of the Hermitian Yang-Mills Equations on Slicewise Stable Bundles

Placement: Professor, Feira de Santana, Brazil

Advisor: Felipe Voloch

Dissertation: Power Series in P-ADIC Roots of Unity

Placement: Mercer Human Resource Consulting, San Francisco, California

Advisor: Fernando Rodriguez-Villegas

Dissertation: A formula for the central value of certain Hecke L-functions

Placement: University of Buenos Aires

Advisor: Elliott Cheney

Dissertation: Theory of Principal Component Filter Banks with Applications to Multicomponent Imagery

Placement: Los Alamos National Labs

Advisor: Luis Caffarelli

Dissertation: Phase Transitions: Regularity of Flat Level Sets

Placement: Post Doctoral Visiting Faculty, University of California at Berkeley

Advisor: Fernando Rodriguez-Villegas

Dissertation: Evaluations of Multiple L-Values and Double Zeta Values of Quadratic Fields

Placement: VIGRE Postdoc, Pennsylvania State University

### Degree Awarded 2002

Advisor: Charles Radin

Dissertation: Density in Hyperbolic Spaces

Current Placement: Zorn Postdoctoral Fellow, Indiana University

Advisor: Karen Uhlenbeck

Dissertation: An Application of The Continuity Method for an Equation on Line Bundles

Placement: Universidade de Federal, Rio de Janeiro, Brazil

Advisor: Haskell Rosenthal

Dissertation: Bounded Operators without Invariant Subspaces on Certain Banach Spaces

Placement: The University of Texas at Austin

Advisor: Panagiotis Souganidis

Dissertation: Uniqueness and Existence Results on Viscosity Solutions of Some Free Boundary Problems

Current Placement: Assistant Professor, University of California at Los Angeles

Advisor: Cameron Gordon

Dissertation: Geodesics in the Complex of Curves of a Surface

Placement: National Security Agency

Advisor: Alan Reid

Dissertation: Essential Surfaces in Hyperbolic Three-Manifolds

Current Placement: Assistant Professor, University of Illinois at Urbana-Champaign

Advisor: Uri Treisman

Dissertation: Collapsing Dimensions, Physical Limitation, and other Student Metaphors for Limit Concepts

Placement: Assistant Professor, Arizona State University

Advisor: Panagiotis Souganidis

Dissertation: On Level Set Approach to Motion of Manifolds of Arbitrary Codimension

Current Placement: Assistant Adjunct Professor, University of California at Los Angeles

Advisor: Mikhail Vishik

Dissertation: Modal Expansions of Surface Wave Model Equations

Current Placement: Assistant Professor, St. Mary's College of Maryland

Advisor: Thaleia Zariphopoulou

Dissertation: On the Merton Problem in Incomplete Markets

Placement: Graduate Research Assistant, The University of Texas at Austin

Advisor: Luis Caffarelli

Dissertation: Plane-like minimal surfaces in periodic media with inclusions

Current Placement: University of Houston

Advisor: Luis Caffarelli

Dissertation: Plane-like Minimizers in Periodic Media: Jet Flows and Ginzburg-Landau

Current Placement: University of Rome III

Advisor: Rafael de la Llave

Dissertation: A Nash-Moser Implicit Function Theorem with Whitney Regularity and Applications

Placement: University of Wisconsin at Madison

Advisor: Jerry Bona and Todd Arbogast

Dissertation: Numerical Schemes for Systems of Non-linear Dispersive Wave Equations

Placement: Visiting Mathematician, Oklahoma State University

### Degree Awarded 2001

Advisor: Hans A. Koch

Dissertation: Renormalization, invariant tori, and periodic orbits for Hamiltonian flows

Placement: McMaster University, Hamilton, Ontario, Canada

Advisor: Lorenzo Sadun

Dissertation: The Topology and Geometry of DNA and DNA-Protein Interaction

Placement: Assistant Professor, Applied Mathematics, Brown University

Advisor: Felipe Voloch

Dissertation: Canonical and Minimal Degree Liftings of Curves

Current Placement: Instructor, Ohio State University

Advisor: Raymond Heitmann

Dissertation: The Plus Closure of an Ideal

Placement: Assistant Professor, St. Joseph's University

Advisor: Jerry L. Bona

Dissertation: Models for Internal Waves in Two-Fluid Systems

Placement: Research Fellow, Norwegian University of Sciences and Technology, Trondheim, Norway

Advisor: David Saltman

Dissertation: Birational Isomorphisms between Severi-Brauer Varieties

Current Placement: Gibbs Assistant Professor, Yale University

Advisor: Ralph Showalter

Dissertation: Fluid Flow and Deformable Multi-Porous Media

Placement: Avaya Communication, Westminster, CO

Advisor: Klaus Bichteler

Dissertation: The L p Theory of Random Measures

Placement: Engineering Scientist, Applied Research Lab, University of Texas at Austin

Advisor: Jerry Bona

Dissertation: Rare events and conditional limit theorems for a class of spectrally positive, heavy-tailed Levy processes

Placement: Visiting Instructor, Macalester College, St. Paul, MN

Advisor: Sean Keel

Dissertation: The Birational Geometry of M3 and M2,1

Placement: VIGRE Postdoc, University of Georgia at Athens

Advisor: Ralph E. Showalter

Dissertation: Heat Transport Models With Distributed Microstructure

Current Placement: Los Alamos National Laboratory

### Degree Awarded 2000

Advisor: David Saltman

Dissertation: Generic Galois extensions for groups of order p^3

Current Placement: Assistant Professor, Florida Atlantic University

Advisor: Jeffrey Vaaler

Dissertation: Estimates for the Number of Polynomial with Bounded Degree and Bounded Measure

Advisor: Sean Keel

Dissertation: Fibrations of the Closure of M_{g,n}

Current Placement: Assistant Professor, University of Pennsylvania

Advisor: Karen Uhlenbeck

Dissertation: Constructing Special Langrangain Cones

Placement: Postdoctoral Assistant Professor, Johns Hopkins University

Advisor: Ralph Showalter

Dissertation: Two Distributed Capacitance Models

Placement: Assistant Professor, Sogang University, Korea

Advisor: Bill Beckner

Dissertation: Sobolev trace inequality and logarithmic Sobolev trace inequality

Placement: Sejong University, Seoul, Korea

Advisor: Cameron Gordon

Dissertation: Essential Surfaces after Dehn Filling

Placement: Assistant Professor, St. Edward's University

Advisor: E.W. Cheney and E. I. George

Dissertation: Proper Posterior Distributions for some Hierarchical models and Roundoff Effects in the Gibbs Sampler

Placement: Research Scientist, Quintiles, Inc.

### Degree Awarded 1999

Advisor: Cameron Gordon

Dissertation: A Piecewise-Linear Theory of Minimal Surfaces of Non-Zero Index

Current Placement: Pitzer College, California

Advisor: Jeffery Vaaler

Dissertation: Analogs of the Beurling-Selberg Functions in N Dimensions and their applications

Current Placement: Birmingham-Southern College

Advisor: Robert Gompf

Dissertation: On a Remarkable Set of Words in the Mapping Class Group

Current Placement: Universidad Nacional de Columbia

Advisor: Felipe Voloch

Dissertation: Diophantine Problems in Function Fields of Positive Characteristic

Current Placement: Inha University, Korea

Advisor: Jose Felipe Voloch

Dissertation: On Lang's diophantive conjecture for surfaces of general type

Current Placement: Texas A&M Univ. at Galveston

Advisor: Lorenzo Sadun

Dissertation: Numerical Investigations of Singularity Formation in Non-Linear Wave Equations in the Adiabatic Limit

Current Placement: Texas A&M Univ.

Advisor: Alan Reid

Dissertation: Lengths and Homology of Hyperbolic 3-Manifolds

Current Placement: Univ. at Buffalo

### Degree Awarded 1998

Advisor: Jeffrey Vaaler

Dissertation: On an Integral Related to Vinogradov's Integral

Placement: United Arab Emirates University

Advisor: Cameron Gordon

Dissertation: The Degeneracy Slopes and the Stretching Factors of Fibered Alternating Knots

Current Placement: Lone Star College

Advisor: Jerry Bona

Dissertation: Solitary Waves and Long-Wave Phenomena

Current Placement: University of Memphis

Advisor: John Tate

Dissertation: Stark's Conjecture in the Octahedral Case

Current Placement: California Lutheran University

Advisor: Lorenzo Sadun

Dissertation: Adiabatic Limits of the Anti-Self-Dual Equation

Advisor: Sean Keel

Dissertation: Segre Class of Almost Complete Intersections

Current Placement: University of Texas at Austin

Advisor: Jeffery Vaaler

Dissertation: An Extremal Majorant for the Logarithm and Its Applications

Current Placement: Northwestern University

Advisor: John Luecke

Dissertation: Manifolds Obtained by Dehn Surgery on Infinitely Many Distinct Knots in s^3

Current Placement: Univ. of Dallas

Advisor: R. de la Llave

Dissertation: Normal Form Techniques in Degenerate Hamiltonian Systems

Current Placement: Oregon Institute of Technology

Advisor: Robert Boyer and Larry Hines

Dissertation: Discoveries and Experiments In the Automation of Mathematical Reasoning

Current Placement: Bethel University

### Degree Awarded 1997

Advisor: David M. Young, Jr.

Dissertation: Iterative Solutions of Large Sparse Nonsymmetric Linear Systems

Current Placement: National Kaohsiung Normal Univ., Korea

Advisor: Peter W. M. John

Dissertation: Optimal Fractional Factorial Designs

Advisor: Jeffery Vaaler

Dissertation: Spectra of Heights over Certain Finite Groups

Current Placement: Washington and Lee Univ.

Advisor: Robert Gompf

Dissertation: Symplectic Constructions on 4-Manifolds

Current Placement: University of Pennsylvania

Advisor: Karen Uhlenbeck

Dissertation: The Cauchy Initial Value Problem for Yang-Mills Metrics

Current Placement: Institute of Technology, Tralee Ireland

Advisor: Elliott Ward Cheney, Jr.

Dissertation: Degree of Approximation by Neural Networks

Advisor: Edward Odell

Dissertation: On Bourgain's Index and Schreier Sets

Current Placement: University of Denver

Advisor: Sean Keel

Dissertation: Exceptional Surfaces For Resolution of Isolated Threefold Singularities

Current Placement: John Hopkins

Advisor: Ralph Showalter

Dissertation: A Coupled System of Semilinear Parabolic Equations with Hysteresis

Current Placement: University of Washington

Advisor: Cameron Gordon

Dissertation: Exceptional manifolds After Dehn Filling

Placement: Mathematical Sciences Research Institute

Advisor: Cameron Gordon

Dissertation: Heegaard Surfaces and Dehn Fillings: G(M)-1 Less than T(X) Less than G(M)

Current Placement: University of Arkansas

Advisor: Cameron Gordon

Dissertation: On the Classification and Stabilization Problems for Heegaard Splittings of Three-Manifolds

Current Placement: Depaul Univ.

Advisor: Alec Norton

Dissertation: Cantor Sets and Lipschitz Actions on Circles and Trees

Current Placement: Diego Corp., Palo Alto

### Degree Awarded 1996

Advisor: H. Rosenthal

Dissertation: Isomorphically Polyhedral Banach Spaces and Mixed Tsirelson Spaces of Arbitrary Distortion

Placement: Univ. of Missouri

Advisor: Edward Odell

Dissertation: On James Spaces

Current Placement: University of Texas at Austin

Advisor: Jeffery Vaaler

Dissertation: Diophantine Approximation on Projective Spaces over Number Fields

Placement: Princeton Institute for Advanced Study

Advisor: Peter W. M. John

Dissertation: Construction of Time Trend Free Run Orders

Advisor: Cameron Gordon

Dissertation: Hyperbolic Knots with Small Seifert-fibered Dehn Surgeries.

Placement: Mathematical Sciences Research Institute

Advisor: Charles Radin

Dissertation: Ergodic Theory, X-Ray Diffraction and Tilings of Euclidean Space

Placement: Rice University

Advisor: William Beckner

Dissertation: Percolation on the Randomized Sierpinski Carpet

Placement: Univ. of Texas, Austin

Advisor: Robert Gompf

Dissertation: Distinguishing Embedded Curves in Rational Complex Surfaces

Placement: Univ. of Calif. at Irvine

Advisor: Haskell Rosenthal

Dissertation: Quotients of C(K) Spaces

Current Placement: University of Crete

Advisor: William Beckner

Dissertation: Sharp Moser Inequalities

Placement: Korea University, Instructor

Advisor: John Tate

Dissertation: On Refined Class Number Formula

Placement: Ohio State

Advisor: Charles Radin

Dissertation: The Topological and Geometrical Properties of a Uniquely Ergodic Tiling System

Advisor: David Saltman

Dissertation: Global Sections of Higher Powers of the Twisting Sheaf on a Brauer-Severi Variety

Placement: Indiana University

Advisor: Elliott Cheney

Dissertation: The Fundamentality Problem for Translates of Continuous Functions

Placement: Korea University

### Degree Awarded 1995

Advisor: Jose Felipe Voloch

Dissertation: Effective p-Descent

Placement: Univ. of Arizona

Advisor: Cameron Gordon

Dissertation: Reducing Spheres and Embedded Projective Planes after Dehn Surgery on a Knot

Placement: Louisiana State University

Advisor: Patrick Brockett

Dissertation: A new approach to sensitivity analysis of the DEA models and its applications in ranking and productivity growth

Advisor: Jeffery Vaaler

Dissertation: Algorithms for the Determination of Polynomials with Small Mahler Measure

Placement: Appalachian State Univ.

### Degree Awarded 1994

Advisor: Jeffery Vaaler

Dissertation: Diophantine Approximation in Local Fields by Algebraic Numbers of Bounded Degree

Placement: Texas A&M Univ., Kingsville

Advisor: Edward Odell

Dissertation: The James Function Space

Placement: Univ. of Wisconsin

Advisor: Peter W. M. John

Dissertation: Optimal and Minimal Experimental Designs

Placement: Institute of Taiwan Studies

Advisor: Elliott Cheney

Dissertation: Cardinal Spline Wavelets

Placement: Oklahoma State University

Advisor: Alec Norton

Dissertation: Self Homeomorphisms of the 2-sphere which pointwise fix a nonseparating continuum

Placement: Mississippi State Univ.

Advisor: John Luecke

Dissertation: On Composite Twisted Unknots

Placement: University of Arkansas

Advisor: Ralph Showalter

Dissertation: Semilinear Degenerate Parabolic Systems and Distributed Capacitance Models

Current Placement: Brentwood Christian School, Austin TX

Advisor: William Schelter

Dissertation: On Automatic Theorem Proving in Conjugate Geometries

Advisor: Raymond Heitmann

Dissertation: Making the Generic Formal Fiber Local

Current Placement: Williams College

Advisor: Ayan Basu

Dissertation: Minimum disparity estimation in linear regression models: robustness and efficiency

Placement: Taejan University, Korea

Advisor: David M. Young, Jr. and Kamy Sepehrnoori

Dissertation: Multigrid Methods with Application in Reservoir Simulation

Placement: Western Atlas, Houston

Advisor: Jeffery Vaaler

Dissertation: The Lagrange Spectrum in Projective Space Over a Local Field

Placement: Univ. of Tennesee

Advisor: Patrick Brockettand and Vijay Mahajan

Dissertation: Stochastic Programming and Optimal Saleforce Compensation Schemes

### Degree Awarded 1993

Advisor: Haskell Rosenthal

Dissertation: Some Subclasses of Baire-1 Functions and Uniform Homeomorphisms

Current Placement: Al Akhawayn University, Morroco

Advisor: Elliott Cheney

Dissertation: Wavelet Analysis in Hilbert Space

Placement: Taiwan University

Advisor: Jeffrey Vaaler

Dissertation: Radial Analogues of some Extremal Beuring-Selberg Functions

Placement: Michigan Tech Univ.

Advisor: Ralph Showalter

Dissertation: Semilinear Parabolic Equations with Preisach Hysteresis

Current Placement: Univ. of Texas at Arlington

Advisor: Karen Uhlenbeck

Dissertation: A Finite Index Approximation of Floer Homology

Current Placement: Texas Legislative Budget Board

Advisor: Cameron Gordon

Dissertation: A Characterization of Handlebodies, Homotopy and Homology Unknotting Numbers of a Knot

Placement: Blackburn College

Advisor: Rafael de la Llave

Dissertation: Rigidity for Dynamically Defined Cantor Sets and Expanding Circle Maps

Current Placement: University of Texas at Austin

Advisor: Edward Odell

Dissertation: Unconditional Averages in the Banach Spaces c(alpha)

Placement: Hanover College

Advisor: Robert Boyer

Dissertation: Automated Proofs of Object Code for a Widely Used Microprocessor

### Degree Awarded 1992

Advisor: Ralph Showalter

Dissertation: Microstructure Modeling of Fluid Flow in a Layered Medium

Current Placement: Mississippi State

Advisor: Ralph Showalter

Dissertation: Diffusion Models with Microstructure and Secondary Flux

Current Placement: Singular Value Consulting

Advisor: David Hinkley

Dissertation: Nonparametric Regression and Its Uses in Checking Model Fit

Current Placement: Lawrence Livermore National Laboratory

Advisor: Abraham Charnes

Dissertation: Senstivity and Stability Analysis of Problems in Chance Constrained Programming

Advisor: Haskell Rosenthal

Dissertation: On Operators in L(L_1).

Placement: Hebei Univ. China

Advisor: E.W. Cheney

Dissertation: Interpolation on Spherical Spaces

Current Placement: University of Sao Paolo

Advisor: Ralph Showalter

Dissertation: The Regularized Layered Medium Equation

Placement: Charleston College

Advisor: Cameron Gordon

Dissertation: Incompressible punctured tori in the complements of alternating knots

Placement: Murray State

Advisor: Jeffrey Vaaler

Dissertation: On the Number of Irreducible Factors of a Polynomial

Current Placement: Univ. of British Columbia, Vancouver

Advisor: Stephen McAdam

Dissertation: Intergral Uppers

Current Placement: University of Calif. at Riverside

Advisor: Robert Williams

Dissertation: The Prime Decomposition of Knotted Periodic Orbits in Dynamical Systems

Current Placement: Northwestern University

Advisor: David M. Young

Dissertation: Parallel Multilevel Iterative Methods

Current Placement: Clark Univ., Georgia

Advisor: David Saltman

Dissertation: Valuations on Division Algebras

Placement: Denison Univ.

Advisor: Abraham Charnes

Dissertation: Optimization of Pursuit and Reliability on Discrete Graphs

### Degree Awarded 1991

Advisor: Cameron Gordon

Dissertation: Essential Laminations in Closed Seifert Fibered Spaces

Placement: Univ. of Puget Sound

Advisor: William Eaton

Dissertation: Three Level Forms in s^4

Current Placement: Fidelity National Information Services

Advisor: Peter W. M. John

Dissertation: Balanced Factorial Structure with the Hypercubic Association Scheme

Advisor: Abraham Charnes

Dissertation: Vector Extremal Approaches to Competitive Models in Economics and Business Activities

Advisor: Cameron Gordon

Dissertation: Linking and Unlinking Properties of Two Component Links

Placement: James Madison

Advisor: Carl Morris

Dissertation: Empirical and Hierarchical Bayes Estimation of Several Means in the Natural Exponential Family

Advisor: Cameron Gordon

Dissertation: Proper Knots are Locally Unknotted and a New Proof of Schubert's Bridge Number Theorem

Placement: Bradley

Advisor: Karen Uhlenbeck

Dissertation: On the Yang-Mills Heat Flow in Two and Three Dimensions

Current Placement: Lund Univ., Sweden

Advisor: David Saltman

Dissertation: Orthogonal Matrix Invariants and Generalized Matrix Concomitants

Placement: Northern Illinois Univ.

Advisor: Abraham Charnes

Dissertation: On a Class of Dual Methods for Quadratic Programming

Advisor: Stephen McAdam

Dissertation: Uppers to (0) in Intersections of Prime Ideals in Polynomial Rings

Placement: Northwest La State

Advisor: Abraham Charnes

Dissertation: On Some Problems of Chance-Constrained Programming

Advisor: Martha Smith

Dissertation: On the Stable Rank of Enveloping Algebras

Current Placement: Univ. of Texas, Corpus Christi

### Degree Awarded 1990

Advisor: William Beckner

Dissertation: Fourier Analysis on the Sierpinski Gasket.

Current Placement: University of Iowa

Advisor: Michael Starbird

Dissertation: The Repovs Conjecture

Current Placement: Wooster College

Advisor: Jeffrey Vaaler

Dissertation: Diophantine Approximation in S-integers

Current Placement: Williams College

Advisor: Abraham Charnes and Patrick Brockett

Dissertation: Chance Constrained Programming and Chebychev Systems with Applications

Advisor: William Schelter

Dissertation: On Some Questions Concerning Weak Identities, Invariants, and Integrality

Advisor: David M. Young, Jr.

Dissertation: Generalized Conjugate Gradient and Lanczos Methods for the Solution of Nonsymmetric Systems of Linear Equations

Current Placement: Los Alamos

Advisor: E. W. Cheney

Dissertation: The condition number and the singularity of a certain interpolation matrix

Advisor: Cameron Gordon

Dissertation: Non-simple ribbon fibered knots

Current Placement: Tokyo Denkii University

Advisor: Jeffrey Vaaler

Dissertation: Small Solutions to Inhomogeneous Systems of Linear Equations Over an Algebraic Number Field

Placement: Seattle Pacific Univ.

Advisor: David M. Young, Jr. and David Kincaid

Dissertation: The Iterative Solution of Large Sparse Linear Systems Using Vector Computers

Current Placement: Cray Research, Minnesota

Advisor: Cameron Gordon

Dissertation: Invariants of Link Cobordism

Current Placement: South Florida University

Advisor: Edward Odell

Dissertation: Sequential Domination in Banach Spaces and the Geometry of JH*

Current Placement: Kenyon College

Advisor: E.W. Cheney

Dissertation: Multivariate Interpolation Using Ridge or Related Functions

Placement: S.W. Missouri State University

Advisor: Cameron Gordon

Dissertation: The Reidemeister and Markov Theorems via Diagrams for Links in 3-Manifolds

Placement: Univ. of Wisconsin

### Degree Awarded 1989

Advisor: William Eaton

Dissertation: Vorticist Denizens of R^3 are tame

Advisor: Efraim P. Armendariz

Dissertation: Isomorphic Ore Extensions of Automorphism Type

Placement: Yeungnam Univ., Korea

Advisor: William Eaton

Dissertation: A New Proof that 1-ULC Implies Tameness

Current Placement: College of Southern Nevada

Advisor: Haskell Rosenthal

Dissertation: On Uniform Structures in Infinite Dimensional Banach Spaces

Current Placement: UT El Paso

Advisor: William Beckner

Dissertation: Sobolev inequalities for ultra spherical polynomials

Current Placement: Mississippi State

Advisor: Cameron Gordon

Dissertation: Degree One Maps between Geometric Three-Manifolds

Current Placement: George Washington University

Advisor: David Hinkley

Dissertation: Accurate and Efficient Double-Bootstrap Methods

Advisor: Jeffrey Vaaler

Dissertation: Inequalities for Heights of Algebraic Subspaces with Applications to Construction of Auxiliary Polynomials

Current Placement: University of Texas at Austin

Advisor: David Hinkley

Dissertation: Saddlepoint Approximations in Statistics, Including Resampling

Current Placement: Texas A&M Univ.

### Degree Awarded 1988

Advisor: Efraim P. Armendariz

Dissertation: Rational Function Skew Fields and Related Topics in Skew Field Theory

Advisor: Cameron Gordon

Dissertation: Surfaces in Three-Manifolds and Three-Manifold Triads

Placement: Ball State

Advisor: Ralph Showalter

Dissertation: Dynamics of Gas Absorption

Advisor: Carl Morris

Dissertation: Multiparameter Estimation in Normal Distributions: The Slightly Unequal Variance Case

Advisor: David Saltman

Dissertation: Function Fields of Generalized Brauer-Severi Varieties

Current Placement: University of Texas at Austin

Advisor: Ralph Showalter

Dissertation: Resolution of a Diffusion Problem Arising in the Flow of Fluids

Placement: Carnegie-Mellon

Advisor: Ralph Showalter

Dissertation: The Continuous Dependence of Solutions to a Cauchy Problem.

Placement: Mississippi State Univ.

### Degree Awarded 1987

Advisor: David Saltman and Martha Smith

Dissertation: Invertible Modules

Advisor: Ralph Showalter

Dissertation: Homogenization of the Layered Medium Equation.

Advisor: David Scott and Alan Cline

Dissertation: Preconditioning Bigenvalue Problems

Advisor: Cameron Gordon

Dissertation: Incompressible Surfaces in Alternating Zink Complements

### Degree Awarded 1986

Advisor: Robert S. Boyer and J. Strother Moore

Dissertation: Proving and Discovering Geometry Theorems Using Wu's Method

Advisor: Carl Morris

Dissertation: Empirical Bayes Statistics: A Comprehensive Theory for Data Analysis

Advisor: Carl Morris

Dissertation: Empirical Bayes Methods for Spatial Data

Advisor: Cameron Gordon

Dissertation: Finite Covers of Haken 3-Manifolds

Advisor: David M. Young

Dissertation: Adaptive Iterative Algorithms for Large Sparse Linear Systems

Advisor: Bruce Palka

Dissertation: Quasiconformal groups and Quasisymmetric Embeddings

Advisor: Cameron Gordon

Dissertation: Heegaard splitting and groups presentations

Advisor: Gary L. Wise

Dissertation: Some Problems in Martingale-Like Operators and Flows of Sigma Algebras Arising in Communication Theory.

Advisor: Ralph Showalter

Dissertation: A Stefan Problem with Prescribed Convection

Advisor: Bruce Palka

Dissertation: On the Laplace-Beltram Operator in Hyperbolic Space

Advisor: William Eaton

Dissertation: Critical Level Embeddings of S^3 in S^4

Advisor: Haskell Rosenthal

Dissertation: The Radon Nikodym Property for Convex Sets.

### Degree Awarded 1985

Advisor: Edward W. Odell

Dissertation: On the Isomorphic Structure of the Stopping Time Banach Space and on the Problem of Best Compact Approximation for Operators Between Lp Spaces.

Advisor: Peter W. M. John

Dissertation: Ordering the Points in Factorial Experiments to Protect against Early Termination

### Degree Awarded 1984

Advisor: Peter W. M. John

Dissertation: D-optimal experimental designs and alternative models for quadratic blending with process variables

Advisor: Andrew J. Casson

Dissertation: On immersed 2-spheres in some 4-manifolds

Advisor: Haskell P. Rosenthal

Dissertation: Properties of Tauberian operators on Banach spaces

Advisor: Graham F. Carey

Dissertation: Adaptive finite element grid generation and extension for elliptic problems posed on unbounded domains

Advisor: Efraim Armendariz

Dissertation: Regular and strongly pi-regular rings

### Degree Awarded 1983

Advisor: Klaus R. Bichteler

Dissertation: A simple version of the Malliavin calculus with applications to the filtering equation

Advisor: Abraham Charnes

Dissertation: Informatics, analysis, and solution of a class of constrained integer network problems

### Degree Awarded 1982

Advisor: Abraham Charnes

Dissertation: On some economic distribution and network problems

Advisor: Howard E. Lacey and John E. Gilbert

Dissertation: On the boundedness of the Banach space-valued Hilbert transform

Advisor: David M. Young, Jr.

Dissertation: Generalized conjugate gradient acceleration of iterative methods

Advisor: Stephen J. McAdam

Dissertation: Asymptotic primes and applications

Advisor: Jeffrey D. Vaaler

Dissertation: Inequalities for character sums

Placement: Rust College, Misissippi

Advisor: Murray R. Cantor

Dissertation: Decomposition of symmetric two-tensors over a compact Riemannian manifold with boundary

Advisor: Abraham Charnes

Dissertation: Goal arc methods in EEO planning and control

### Degree Awarded 1981

Advisor: Michael P. Starbird

Dissertation: Countable cellular decomposition of S^(s)

Advisor: George G. Lorentz

Dissertation: Rolle's theorem for Birkoff systems

Advisor: Ralph E. Showalter

Dissertation: Degenerate evolution equations and inequalities

Advisor: Michael P. Starbird

Dissertation: The theory of block complexes with an application to manifold splittings

Advisor: Peter W. M. John

Dissertation: Trace optimality in non-orthogonal blocking designs of two-level factorial experiments

Advisor: Jeffrey D. Vaaler

Dissertation: Limit theorems for sequences of divisor distributions

Placement: Univ. of Tennesee

### Degree Awarded 1980

Advisor: John E. Gilbert

Dissertation: Conjugate Hankel transforms and Hp-theory

Advisor: Stephen J. McAdam

Dissertation: Prime divisors and the altitude formula

### Degree Awarded 1979

Advisor: John D. Dollard

Dissertation: Quantum-mechanical scattering theory for long-range oscillatory potentials

Advisor: Ralph E. Showalter

Dissertation: Implicit degenerate evolution equations in Hilbert spaces

Advisor: Don E. Edmondson

Dissertation: Unique periodic solutions of a class of differential equations and composite solutions of a system of partial differential equations

Advisor: James W. Vick

Dissertation: Smooth group actions of prime order and fixed point sets

### Degree Awarded 1978

Advisor: Anthony A. Iarrobino

Dissertation: Hilbert functions of vector spaces of forms

Advisor: R. H. Bing

Dissertation: Some properties of patched 2-spheres

Advisor: Klaus R. Bichteler

Dissertation: Sample path properties of continuous local Martingales

Advisor: Charles N. Friedman

Dissertation: Asymptomatic behavior of solutions of the radical Schroedinger equation and applications to long-range potential scattering

### Degree Awarded 1977

Advisor: Ralph E. Showalter

Dissertation: A degenerate evolution equation for fluid flow in multi-porous media

Advisor: Abraham Charnes

Dissertation: Goal interval methods for some problems of economic policy and stabilization

Advisor: R. H. Bing

Dissertation: Stable homeomorphisms on the pseudo-arc

Advisor: Howard E. Lacey

Dissertation: Studies in local unconditional structure in Banach spaces and characterizations of complex predual L1-spaces

Advisor: Newcomb Greenleaf

Dissertation: Difference relations and algebra: a constructive study

Advisor: Ralph E. Showalter

Dissertation: Galerkin approximation of some nonlinear partial differential equations modeling long waves in shallow water

Advisor: Abraham Charnes

Dissertation: Entropic solutions and disruption solutions for n-person games

Advisor: Peter W. M. John

Dissertation: Topics in partially balanced designs

### Degree Awarded 1976

Advisor: John R. Durbin

Dissertation: Wreath products with supersolvable automorphism groups

### Degree Awarded 1975

Advisor: Larry L. Schumaker

Dissertation: Discrete polynomial spline approximation methods

Advisor: Newcomb Greenleaf

Dissertation: Automorphism groups of compact Klein surfaces with boundary

Advisor: Newcomb Greenleaf

Dissertation: Fundamental domains and projective structures on compact Klein surfaces

Advisor: Abraham Charnes

Dissertation: Topics in network scheduling

### Degree Awarded 1974

Advisor: Larry L. Schumaker

Dissertation: Structure and characterization of pLq-splines

Advisor: John R. Cannon

Dissertation: The numerical approximation of certain parabolic equations backward in time via Sobolev equations

Advisor: John R. Durbin

Dissertation: Representations of wreath products

Advisor: John E. Gilbert

Dissertation: Harmonic analysis on SO(3)

Advisor: Elliott Ward Cheney, Jr.

Dissertation: Optimization of the Lagrange interpolation process

Advisor: John E. Gilbert

Dissertation: Topics in harmonic analysis with applications to abstract Besov and Sobolev spaces

Advisor: John E. Gilbert

Dissertation: Stone-Weierstrass properties in some commutative Banach algebras

### Degree Awarded 1973

Advisor: Robert E. Greenwood

Dissertation: On a Menger graph distance problem

Advisor: Stephen J. McAdam

Dissertation: Chains of primes in a Noetherian domain

Advisor: Peter W. M. John

Dissertation: On resistance of balanced incomplete block designs

Advisor: William T. Guy, Jr.

Dissertation: On tensors and extensors having complex components

### Degree Awarded 1972

Advisor: Sterling. K. Berberian

Dissertation: On maximal rings of quotients of finite Baer*-rings

Advisor: Robert E. Greenwood

Dissertation: Numerical integration facilitated by polynominals in e(^x)

Advisor: George G. Lorentz

Dissertation: Interpolation of operators in function spaces

Advisor: Abraham Charnes

Dissertation: A mathematical theory of coalitions and Competition in Resource Development

Advisor: Howard E. Lacey and Hubert S. Wall

Dissertation: Some summability theorems concerning a certain class of sequences

### Degree Awarded 1971

Advisor: John R. Durbin

Dissertation: Conjugacy theorems in locally finite groups

Advisor: Howard V. Craig

Dissertation: On certain extensor structures in the calculus of variations

Advisor: Woodrow W. Bledsoe

Dissertation: Locking: a restriction of resolution

Advisor: Robert E. Greenwood

Dissertation: Group exponential polynominals and enumeration of paths on a lattice

Advisor: Abraham Charnes

Dissertation: Non-cooperative game theory and industrial competition

Advisor: Galen L. Seever

Dissertation: Contractive projections in abstract Banach function spaces

Advisor: William T. Guy, Jr.

Dissertation: A generalized Mellin transform

Advisor: Hubert S. Wall

Dissertation: Concerning continued fractions

Advisor: David M. Young, Jr.

Dissertation: An analysis of a class of norms of iterative methods for systems of linear equations

Advisor: Efraim Armendariz

Dissertation: Maximal quotient rings and S-rings

Advisor: Howard E. Lacey

Dissertation: On some classes of Banach spaces whose duals are abstract L-spaces

Advisor: Don E. Edmondson

Dissertation: Modularity and decomposition of semilattices

Advisor: William T. Guy, Jr.

Dissertation: Laplace-Stieltjes transform of Mikusinski operator functions

### Degree Awarded 1970

Advisor: Elliott Ward Cheney, Jr.

Dissertation: Extensions and projections in spaces of continuous functions

Advisor: Woodrow W. Bledsoe

Dissertation: Some theoretical aspects of automatic theorem proving

Advisor: Robert E. Greenwood

Dissertation: The rectilinear crossing number for complete simple graphs in E2

Advisor: John R. Durbin

Dissertation: Groups with a characteristic cyclic series

Advisor: Robert T. Gregory

Dissertation: Preliminary investigations using interval arithmetic in the numerical evaluations of polynomials

Advisor: Hubert S. Wall

Dissertation: Concerning linear and nonlinear sequence to sequence transformations

Advisor: Robert E. Greenwood

Dissertation: Finite sets with special minimal properties

Advisor: Hubert S. Wall

Dissertation: On length and variation of simple graphs

Advisor: Efraim Armendariz

Dissertation: Restricted semiprimary rings

Advisor: Abraham Charnes

Dissertation: Goal programming and satisficing models in economic analysis

Advisor: David M. Young, Jr.

Dissertation: A multiplicity-independent, global iteration for meromorphic functions

Advisor: Roy P. Kerr

Dissertation: p-points in topological spaces

Advisor: Robert E. Greenwood

Dissertation: Numerical integration of analytic functions

Advisor: Elliott Ward Cheney, Jr.

Dissertation: Projections and approximation in a normed linear space

Advisor: David M. Young, Jr.

Dissertation: Finite-difference methods for a harmonic mixed boundary value problem

### Degree Awarded 1969

Advisor: William T. Guy, Jr.

Dissertation: On properties of certain testing spaces

Advisor: Milo W. Weaver

Dissertation: Orbit-like relations on binary and N-ary groups

Advisor: Hubert S. Wall

Dissertation: Concerning Stieltjes Integrals

Advisor: William T. Guy, Jr.

Dissertation: Generalized functions of two discrete variables

Advisor: R. L. Moore

Dissertation: Concerning certain plane-like domains

Advisor: Robert T. Gregory

Dissertation: Bounds and location theorems of the Eigenvalues of matrices partitioned into blocks

Advisor: Abraham Charnes

Dissertation: On some unimodular and boolean mathematical programming problems

Advisor: Don E. Edmondson

Dissertation: The structure of Hjelmslev space: a generalization of projective space

Advisor: Hubert S. Wall

Dissertation: On Baire systems of functions

Advisor: Hubert S. Wall

Dissertation: Concerning simple graphs dense in the plane

Advisor: Hubert S. Wall and R. L. Moore

Dissertation: Some separation theorems

Advisor: Hubert S. Wall

Dissertation: Convergence regions and value regions for continued fractions

Advisor: John R. Durbin

Dissertation: Factor coverings of groups

Advisor: Don E. Edmondson

Dissertation: Some results in Brouwerian lattices

Advisor: R. L. Moore

Dissertation: Concerning indecomposable continua and upper semi-continuous

Advisor: Woodrow W. Bledsoe

Dissertation: The regularity of a product measure using regular conditional measure

### Degree Awarded 1968

Advisor: Howard E. Lacey

Dissertation: A study of left-prime ideals in topological rings

Advisor: Elliott Ward Cheney, Jr.

Dissertation: Some uncomplemented subspaces of C(X) of the type C(Y)

Advisor: Howard E. Lacey

Dissertation: Compact convex sets and continuous affine functions

Advisor: Hubert S. Wall

Dissertation: Existence of product integrals

Advisor: William T. Guy, Jr.

Dissertation: Infinite series transformations and their applications

Advisor: Hubert S. Wall

Dissertation: Inner product-type transformations

Advisor: Hubert S. Wall

Dissertation: Concerning an integral and number sets dense in an interval

Advisor: William T. Guy, Jr.

Dissertation: The two-dimensional Z transform with real domain and parameters

Advisor: Howard E. Lacey

Dissertation: Functors in categories of Banach spaces

Advisor: Robert E. Greenwood

Dissertation: Pseudo-mixing sequences of random variables

Advisor: Hubert S. Wall

Dissertation: Concerning pointwise discontinuous functions

Advisor: R. L. Moore

Dissertation: Concerning the separation of certain plane-like spaces by compact dendrons

Advisor: Howard E. Lacey

Dissertation: Spaces of Affine continuous functions

Advisor: Howard E. Lacey

Dissertation: Regular Borel measures on compact spaces

Advisor: William T. Guy, Jr.

Dissertation: An operational calculus on real valued set functions

Advisor: H. J. Ettlinger

Dissertation: On the Perron integral and solutions to partial differential equations

Advisor: Howard B. Curtis, Jr.

Dissertation: Some normal families of rational functions

Advisor: H. J. Ettlinger

Dissertation: Perron type differential and integral inequalities

Advisor: R. L. Moore

Dissertation: Concerning uncountable collections of mutually exclusive compact continua

Advisor: Hubert S. Wall

Dissertation: On a generalization of continuity

Advisor: Howard B. Curtis, Jr.

Dissertation: Rings of analytic functions

Advisor: William T. Guy, Jr.

Dissertation: Numerical calculation of the Laplace transform by the use of Legendre polynomials

Advisor: Elliott Ward Cheney, Jr.

Dissertation: On the (beta)-topology on C(X)

### Degree Awarded 1967

Advisor: Hubert S. Wall

Dissertation: Concerning connected simple graphs

Advisor: Robert T. Gregory

Dissertation: Matrix scaling with respect to the maximum-norm, the sum-norm,

Advisor: Hubert S. Wall

Dissertation: A theorem concerning product integrals

Advisor: R. L. Moore

Dissertation: Concerning compact point sets with noncompact closures

Advisor: Hubert S. Wall

Dissertation: Certain linear transformations in a space of functions of two variables

Advisor: Roy P. Kerr

Dissertation: Killing vectors in empty, algebraically special Einstein manifolds with diverging ray congruences

Advisor: Roy P. Kerr

Dissertation: Homogeneous dust filled cosmological models

Advisor: Howard E. Lacey

Dissertation: Compact Hausdorff spaces which are supports of regular Borel measures

Advisor: Hubert S. Wall

Dissertation: Bounded slope variation and the Hellinger integral

Advisor: Howard B. Curtis, Jr.

Dissertation: Representation of uniformizing functions for certain simply and doubly connected Riemann surfaces

Advisor: Howard B. Curtis, Jr.

Dissertation: Fatou values of normal subharmonic functions

Advisor: Homer V. Craig

Dissertation: Contributions to the theory of higher degree extensors and related topics

Advisor: Don E. Edmondson

Dissertation: Homomorphic images of compactly generated lattices

Advisor: R. L. Moore

Dissertation: Holes in two-dimensional space

Advisor: Hubert S. Wall

Dissertation: Concerning lengths for continuous and noncontinuous curves

Advisor: Hubert S. Wall

Dissertation: A characterization of inner product spaces

Advisor: Hubert S. Wall

Dissertation: A representation theorem for bounded linear functionals

### Degree Awarded 1966

Advisor: Patrick L. Odell

Dissertation: Contributions to the theory of pseudo inverses

Advisor: Homer V. Craig

Dissertation: Contribution to the theory of extensive differentiation and related topics

Advisor: Milo W. Weaver

Dissertation: A lattice of partitions on a group

Advisor: Don E. Edmondson

Dissertation: Compact integral domains with finite characteristic

Advisor: R. L. Moore

Dissertation: Concerning the sides from which certain sequences of arcs converge to a compact irreducible continuum

Advisor: Don E. Edmondson

Dissertation: (f)-derivations on a ring

Advisor: Patrick L. Odell

Dissertation: Contributions to the theory of numerical simulation

Advisor: David M. Young, Jr.

Dissertation: Error bounds on numerical solutions of Dirichlet problems for quasilinear elliptic equations

Advisor: William T. Guy, Jr.

Dissertation: The Holmgren-Riesz transform and its applications

Advisor: Clarence Coates, Jr. and Patrick L. Odell

Dissertation: Realization of sequential machines with threshold elements

Advisor: Hubert S. Wall

Dissertation: Concerning sequence to sequence transformations

Advisor: Elliott Ward Cheney, Jr.

Dissertation: A study of operators in approximation theory

Advisor: H. J. Ettlinger

Dissertation: Concerning the nonlinear differential equations H^1 (x)= f(x;H(x)), with elements in E^2

Advisor: Patrick L. Odell

Dissertation: Application of the theory of generalized matrix inversion to statistics

Advisor: Don E. Edmondson

Dissertation: A structure problem in asymptotic analysis

Advisor: Don E. Edmondson

Dissertation: Automorphisms of a class of finite groups

Advisor: Patrick L. Odell

Dissertation: Weighted generalized inverses with minimal p and q norms

Advisor: William T. Guy, Jr.

Dissertation: Numerical inversion of the Laplace transform by the use of Jacobi polynomials

Advisor: Hubert S. Wall

Dissertation: A substitution theorem for a Stieltjes integral

Advisor: Howard E. Lacey

Dissertation: Spaces of continuous functions on dispersed sets

Advisor: Hubert S. Wall

Dissertation: Pointwise limits of sequences of continuous functions

Advisor: Hubert S. Wall

Dissertation: Concerning pointwise limits of sequences of functions

Advisor: Hubert S. Wall

Dissertation: Concerning the value regions associated with a certain type of continued fraction

Advisor: R. L. Moore

Dissertation: A space whose regions are the simple domains of another space

Advisor: Don E. Edmondson

Dissertation: Congruences on an inverse semigroup

Advisor: R. L. Moore

Dissertation: Reversibly continuous bisensed transformations of an annulus into itself

Advisor: William T. Guy, Jr.

Dissertation: Block partitioned matrix theory and solution of systems of certain partial differential equations

Advisor: Hubert S. Wall

Dissertation: Linear transformations in a function space

Advisor: Patrick L. Odell

Dissertation: Interval estimation of a stimulus levels of order infinity in sensitivity testing

Advisor: Hubert S. Wall

Dissertation: Pointwise limits of quasi-continuous functions

Advisor: H. J. Ettlinger

Dissertation: An integral equation and the related differential equation boundary problem

Advisor: Elliott Ward Cheney, Jr.

Dissertation: Continuity of metric projections' approximation theory in a normed linear lattice

### Degree Awarded 1965

Advisor: R. L. Moore

Dissertation: Concerning uncountable collections of triods

Advisor: Don E. Edmondson

Dissertation: On the lattice of continuous functions on a completely regular G(d)-space

Advisor: Robert T. Gregory

Dissertation: A model for a fact retrieval system

Advisor: William T. Guy, Jr.

Dissertation: A generalization of the finite Fourier transformations

Advisor: Hubert S. Wall

Dissertation: A generalization of the real-number axioms

Advisor: Robert T. Gregory

Dissertation: Syntax-directed translation for experimental programming languages

Advisor: R. L. Moore

Dissertation: Concerning upper semi-continuous collections of finite point sets

Advisor: H. J. Ettlinger

Dissertation: Operation solution of partial derivative equations of hyperbolic and parabolic type

Advisor: Hubert S. Wall

Dissertation: Uniform completeness of sets generated by a single function

### Degree Awarded 1964

Advisor: Hubert S. Wall

Dissertation: Orthogonality in normed linear spaces

Advisor: William T. Guy, Jr.

Dissertation: A generalization of the Laplace transform

Advisor: James E. Scroggs

Dissertation: A Banach algebra of analytic functions

Advisor: Hubert S. Wall

Dissertation: Cauchy sequences in abstract spaces

Advisor: H. J. Ettlinger

Dissertation: On the Abel equation in n-dimensions, n equal or more than 2

Advisor: Robert E. Greenwood

Dissertation: Concerning certain lattice paths and lattice point theorems

Advisor: Don E. Edmondson

Dissertation: Psuedo-Metric axioms of a Euclidean geometry

Advisor: Robert T. Gregory

Dissertation: On the tridiagonalizaton of a non-Hermitian matrix using similarity transformations

Advisor: H. J. Ettlinger

Dissertation: On the mixed partial derivative operator and its inverse

Advisor: Alfred Schild

Dissertation: Degenerate fields with twisting rays

### Degree Awarded 1963

Advisor: H. B. Curtis

Dissertation: A class of Riemann surfaces

Advisor: Hubert S. Wall

Dissertation: Concerning Completely Convex Sets

Advisor: Don E. Edmondson

Dissertation: Structure theorems for a class of groups

Advisor: Hubert S. Wall

Dissertation: A study of the structure of linear spaces

Advisor: Hubert S. Wall

Dissertation: Some Theorems on functional analysis

Advisor: David M. Young, Jr.

Dissertation: The Block Symmetric Successive Overrelaxation Method

Advisor: H. J. Ettlinger

Dissertation: Some Generalized Green's Functions

Advisor: Hubert S. Wall

Dissertation: Concerning a Functional Inequality

Advisor: Hubert S. Wall

Dissertation: Concerning a mean integral

Advisor: William T. Guy, Jr.

Dissertation: A class of integral transforms for functions which are O(e^bt2 ) as t-> infinity

Advisor: Hubert S. Wall

Dissertation: An Integral of a function with respect to a function in a rectangular interval

### Degree Awarded 1962

Advisor: Hubert S. Wall

Dissertation: On Sequence to Sequence Transformations

Advisor: R. L. Moore

Dissertation: On the most general plane closed point set through which it is possible to pass a pseudo-arc

Advisor: Hubert S. Wall

Dissertation: Integral Equations in Normed Abelian Groups

Advisor: Don E. Edmondson

Dissertation: Structure theorems for Boolian Matrices

Advisor: H. B. Curtis

Dissertation: On the problem of Type and the Uniformizing Function for Certain Riemann Surfaces

Advisor: H. B. Curtis

Dissertation: A Topological space of analytic functions

Advisor: R. E. Lane

Dissertation: The integral of a function with respect to a function pair

Advisor: William T. Guy, Jr.

Dissertation: A Representation Theorem for the Laplace Transform

### Degree Awarded 1961

Advisor: Hubert S. Wall

Dissertation: Concerning the uniform polynomial approximation of a bounded function

Advisor: Hubert S. Wall

Dissertation: Solutions of analytic equations and solutions of first order, analytic differential equations

Advisor: R. E. Greenwood

Dissertation: Some Marginal Distributions associated with permutation cycles

Advisor: Hubert S. Wall

Dissertation: A convergence problem for continued fractions

Advisor: H. J. Ettlinger

Dissertation: Relationships and analogue between the finite calculus and the limit calculus of polynomials

Advisor: H. J. Ettlinger

Dissertation: An Existence and Uniqueness Theorem for Integro-partial differential equations

### Degree Awarded 1960

Advisor: William T. Guy, Jr.

Dissertation: On Inversion of the Laplace Transformation by means of a step function

Advisor: Hubert S. Wall

Dissertation: Concerning polynomial sequences and the distribution of their zeros

Advisor: H. J. Ettlinger

Dissertation: Solutions of a system of two nonlinear partial differential equations of the first order, with accessory boundary equations

Advisor: Alfred Schild

Dissertation: On the consequences of momentum conservation laws in a gravitational theory of the Whitehead type

Advisor: R. E. Lane

Dissertation: A Hellinger Integral representation for bounded linear functionals

### Degree Awarded 1959

Advisor: R. L. Moore

Dissertation: Proof that every compact continuum which is topologically equivalent to each of its nondegenerate subcontinua is an arc

### Degree Awarded 1958

Advisor: H. J. Ettlinger

Dissertation: Operator matrices and systems of linear partial differential equations

Advisor: Hubert S. Wall

Dissertation: Some convergence theorems for continued fractions

Advisor: R. L. Moore

Dissertation: Concerning locally peripherally separable spaces

Advisor: H. J. Ettlinger

Dissertation: Absolutely continuous solutions of Uxy=f(x,y,u,u_x ,u_y )

Advisor: Hubert S. Wall

Dissertation: Concerning the Hausdorff inclusion problem

Advisor: R. L. Moore

Dissertation: Concerning dense metric subspaces of certain nonmetric spaces

### Degree Awarded 1957

Advisor: H. J. Ettlinger

Dissertation: Interated Holmgren-Riesz transforms in two dimensions

Advisor: Hubert S. Wall

Dissertation: Continued fractions with absolutely convergent even or odd part

Advisor: H. S. Vandiver

Dissertation: Interrelations between the numbers of Bell, Bernoulli, Euler, Fibonacci, and Lucas

Advisor: R. L. Moore

Dissertation: A theorem on spirals in plane

Advisor: Hubert S. Wall

Dissertation: Continuous products and nonlinear integral equations

### Degree Awarded 1956

Advisor: E. W. Titt

Dissertation: Integration formulae and boundary conditions for the hyperbolic differential equation with three independent variables and regions interior to the cone

Advisor: Hubert S. Wall

Dissertation: Some convergence sets for a continued fraction

Advisor: H. S. Vandiver

Dissertation: The application of cosets and correspondence in the theory of semi-groups

### Degree Awarded 1955

Advisor: E. W. Titt

Dissertation: Integration formulae and boundary conditions for the elliptic parabolic partial differential equation with three independent variables

Advisor: William T. Guy, Jr.

Dissertation: On the Hankel transform

Advisor: R. L. Moore

Dissertation: Concerning spirals in the plane

Advisor: R. L. Moore

Dissertation: A connected point set in the plane which spirals down on each of its points

Advisor: E. W. Titt

Dissertation: Integration formulae and boundary conditions for the hyperbolic equation with three independent variables and regions exterior to the cone

### Degree Awarded 1954

Advisor: H. J. Ettlinger

Dissertation: Partial integro-differential equations and the H-R transform

Advisor: H. S. Vandiver

Dissertation: Generating functions for restricted partitions and the Von Sterneck number

Advisor: E. W. Titt

Dissertation: Integration formulae for the hyperbolic partial differential equation with four independent variables and regions interior to the cone

Advisor: William T. Guy, Jr. and Homer V. Craig

Dissertation: Stieltjes integral representation of convex functions

### Degree Awarded 1953

Advisor: H. J. Ettlinger

Dissertation: A second-order theory for three-dimensional wings in supersonic flow

Advisor: R. L. Moore

Dissertation: Flat spaces for which the Jordan curve theorem holds true

### Degree Awarded 1952

Advisor: R. L. Moore

Dissertation: Concerning continuous and equicontinuous collections of arcs

Advisor: R. L. Moore

Dissertation: Certain conditions under which the sum of the elements of a

Advisor: R. L. Moore

Dissertation: Concerning webs in the plane

Advisor: Hubert S. Wall

Dissertation: Uniform completeness of sets of reciprocals of linear functions

### Degree Awarded 1951

Advisor: H. J. Ettlinger

Dissertation: Holmgren-Riesz transform

Advisor: H. J. Ettlinger

Dissertation: Ordinary differential equations of non-integral order

Advisor: R. L. Moore

Dissertation: Concerning continua and their complementary domains in the plane

Advisor: H. S. Vandiver

Dissertation: On the number of solutions of some general types of equations in a finite field

Advisor: Hubert S. Wall

Dissertation: Continued fractions in which the elements are operators in a linear space

### Degree Awarded 1950

Advisor: Hubert S. Wall

Dissertation: Some convergence regions for a continued fraction

Advisor: Hubert S. Wall

Dissertation: Sequences of points in the complex plane

Advisor: Simpson Brown

Dissertation: The investigation of mathematical functions with a harmonic synthesizer

### Degree Awarded 1949

### Degree Awarded 1948

Advisor: R. L. Moore

Dissertation: Concerning upper semi-continuous collections of continua

### Degree Awarded 1947

### Degree Awarded 1945

### Degree Awarded 1942

Advisor: R. L. Moore

Dissertation: Concerning the outer boundaries of certain connected domains

### Degree Awarded 1941

Advisor: H. S. Vandiver

Dissertation: Substitutes for the commutative law in the theory of semi-groups

Advisor: R. L. Moore

Dissertation: On compact unicoherent continua

Advisor: R. L. Moore

Dissertation: Concerning triodic continua

Advisor: R. L. Moore

Dissertation: I. Proper and reductive transformations. II. Continua obtained from sequences of simple chains of point sets. III. Distance axioms in Moore spaces. IV. Linear metric space. V. A space in which there may exist uncountable convergent sequences of points

### Degree Awarded 1939

Advisor: E. G. Keller

Dissertation: The double-slot, salient field pole problem of the dynamo-electric machine

Advisor: H. J. Ettlinger

Dissertation: The oscillation of solutions of the general self-adjoint differential equation of the fourth order with special boundary conditions

Advisor: S. L. Brown__

Dissertation: Solution of analytic and differential equations by harmonic processes

### Degree Awarded 1937

Advisor: H. J. Ettlinger

Dissertation: Non-unique solutions of first order ordinary differential equations

### Degree Awarded 1935

Advisor: R. L. Moore

Dissertation: Concerning R. L. Moore's Axiom 5_1

### Degree Awarded 1933

### Degree Awarded 1932

Advisor: R. L. Moore

Dissertation: Spaces in which there exists contiguous points

Advisor: R. L. Moore

Dissertation: Spaces in which there exist uncountable

### Degree Awarded 1931

Advisor: H. J. Ettlinger

Dissertation: A study of the mathematical processes used in sixteen gainful occupations in Nashville, Tennessee

### Degree Awarded 1930

Advisor: R. L. Moore

Dissertation: On the existence of acyclic curves satisfying certain conditions with respect to a given continuous curve

Advisor: R. L. Moore

Dissertation: Some metric properties of descriptive planes

### Degree Awarded 1929

Advisor: H. J. Ettlinger

Dissertation: Properties of Solutions of an Infinite System of Ordinary Linear Differential Equations of the First Order with Auxiliary Boundary Conditions

Advisor: R. L. Moore

Dissertation: Concerning non-dense plane continua

### Degree Awarded 1927

Advisor: R. L. Moore

Dissertation: Concerning continua in the plane

Advisor: H. J. Ettlinger

Dissertation: Linear boundary value problems for ordinary differential equations and their associated difference equations

### Degree Awarded 1925

Advisor: R. L. Moore

Dissertation: The double elliptic case of the Lie-Riemann-Helmholtz-Hilbert problem of the foundations of geometry.

### Degree Awarded 1923

### Degree Awarded 1916

Advisor: H. J. Ettlinger, M. B. Porter, E. L. Dodd

Dissertation: Functions of limited variation and Lebesgue integrals