Department of Mathematics

Our Ph.D. Graduates

• 2024 Graduates

  James Alcala
  Dissertation Title: “New Classes of Moving Anchor Extragradient
  Algorithms for Saddlepoint Problems”
  Faculty Advisor(s): Yat Tin Chow

   

  Cecilia Duran
  Dissertation Title: “Mathematical Modeling of Hair Follicle Regeneration
  Dynamics and of Polarization Initiation”
  Faculty Advisor(s): Qixuan Wang and Weitao Chen

   

  Jacob Garcia
  Dissertation Title: “Conicality of Morse Limit Sets and Stability”
  Faculty Advisor(s): Matthew Durham

   

  Anthony Muljat
  Dissertation Title: “Representations of FI-Like Categories Associated to
  Subgroups of Wreath Products”
  Faculty Advisor(s): Wee Liang Gan

   

  Matthew Overduin
  Dissertation Title: “Fractional Taylor Series Expansions for Classes of
  Generalized Fractal Strings”
  Faculty Advisor(s): Michel Lapidus

   

  Thomas Schellhous
  Dissertation Title: “Striated Regularity of Vorticity in a Bounded Domain”
  Faculty Advisor(s): James Kelliher

   

  Alysha Toomey
  Dissertation Title: “Multiscale Models for Developing Tissues or Organs in
  Biological Systems”
  Faculty Advisor(s): Weitao Chen and Mark Alber

   

  Gabrielle Tsai
  Dissertation Title: “A Characterization of Bounded Convex Domains in C^n with Non-Compact Automorphism Group”
  Faculty Advisor(s): Bun Wong

• 2023 Graduates

  Savanna Gee
  Dissertation Title: "Synge's Theorem, Systole, and Positive Intermediate Ricci Curvature"
  Faculty Advisor(s): Frederick Wilhelm

   

  Khoa Ta
  Dissertation Title: "Finite Regularity of VIn- Modules"
  Faculty Advisor(s): Wee L. Gan

   

  Christian Williams
  Dissertation Title: "The Metalanguage of Category Theory"
  Faculty Advisor(s): John C. Baez

   

  Noble Williamson
  Dissertation Title: "Birational geometry of blowups of toric projective varieties"
  Faculty Advisor(s): Jose Gonzalez

• 2022 Graduates

  Jonathan Alcaraz
  Dissertation Title: "Surface Bundles Over Low-Dimensional Manifolds"
  Faculty Advisor(s): Stefano G. Vidussi

   

  Gefei Chen
  Dissertation Title: "Information Gathering Problem in Ad-Hoc Radio Networks With Layer Topology"
  Faculty Advisor(s): Kevin Costello

   

  Jonathan P. Dugan
  Dissertation Title: "Demazure Modules and Fusion Products for the Current Algebra sln+1[t]"
  Faculty Advisor(s): Vyjayanthio Chari

   

  Gabriel Elvin
  Dissertation Title: "Avoiding Monochromatic Solutions to Linear Equations"
  Faculty Advisor(s): Kevin Costello

   

  Therese-Marie B. Landry
  Dissertation Title: "Design and Optimization of a Composite Heat Spreader to Improve the Thermal Management of Three-Dimensional Integrated Circuits"
  Faculty Advisor(s): Micheal L. Lapidus

   

  Michael L. McNulty
  Dissertation Title: "On the Stability of Self-Similar Blow-Up in Nonlinear Wave Equations"
  Faculty Advisor(s): Po-Ning Chen, Birgit Schorkhuber

   

  Christian T. Michael
  Dissertation Title: "Mathematical Modeling Study of the Impacts of Boundary Conditions and a Pseudo-3D Mechanism on the Maintenance of the Shoot Apical Meristem of Arabidopsis thaliana"
  Faculty Advisor(s): Mark Alber

   

  Nicholas J. Newsome
  Dissertation Title: "Bounded Domains on Kobayashi Hyperbolic Manifolds Covering Compact Complex Manifolds"
  Faculty Advisor(s): Bun Wong

   

  Adam D. Richardson
  Dissertation Title: "The Complex Dimensions of Space-Filling Curves"
  Faculty Advisor(s): Michael L. Lapidus

   

  Alexander S. Rowell
  Dissertation Title: "Existence and Structure of P-Area Minimizing Surfaces"
  Faculty Advisor(s): Amir Moradi Fam

   

  Benjamin J. Russell
  Dissertation Title: "Linear SCY Groups With Virtual First Betti Number Equal to Four"
  Faculty Advisor(s): Stefano G. Vidussi

   

  Maranda N. Smith
  Dissertation Title: "Macdonald Polynomials and Graded Characters of Generalized Demazure Modules of so(2n)[t]"
  Faculty Advisor(s): Vyjayanthi Chari

   

  Ryan J. Ta
  Dissertation Title: "Ricci Flow Does Not Necessarily Preserve Positive Radial Sectional Curvature"
  Faculty Advisor(s): Frederick Wilhelm

   

  Chulan Zeng
  Dissertation Title: "Time Analyticity of Several Evolutionary Partial Differential Equations"
  Faculty Advisor(s): Qi S. Zhang

• 2021 Graduates

  Kateryna Alkorn
  Dissertation Title: "Correspondence Between the Spectrum of Jacobi Operator and Dominated Splitting of its Cocycle Map"
  Faculty Advisor(s): Zhenghe Zhang

   

  Ethan Kowalenko
  Dissertation Title: "Representation Theory for Oriented Matroids and Combinatorial Intersection Homology for Gorenstein* Meet- Semilattices"
  Faculty Advisor(s): Carl Mautner

   

  Robert Lopez
  Dissertation Title: "Stability of Current Density Impedance Imaging and Uniqueness for the Inverse Sturm-Liouville Problem"
  Faculty Advisor(s): Amir Moradi Fam

   

  Derek Lowenberg
  Dissertation Title: "Representations of Some Categories of FI Type"
  Faculty Advisor(s): Wee Gan

   

  Alexander Martin
  Dissertation Title: "Boundary Asymptotics for Convex and Strongly Pseudoconvex Domains"
  Faculty Advisor(s): Bun Wong

   

  Jade Master
  Dissertation Title: "Composing Behaviors of Networks"
  Faculty Advisor(s): John C. Baez

   

  Alexander Pokorny
  Dissertation Title: " Dubrovnik Skein Theory and Power Sum Elements"
  Faculty Advisor(s): Peter Samuelson

• 2020 Graduates

  Taylor Baldwin
  Dissertation Title: "Solutions to the 2D Euler Equations Satisfying the Serfati Condition With Relaxed Constraints on the Initial Vorticity"
  Faculty Advisor(s): James P. Kelliher

   

  Jolene Britton
  Dissertation Title: "High Order Numerical Methods for Hyperbolic Balance Laws: Well-Balanced Discontinuous Galerkin Methods and Adjoint- Based Inverse Algorithms"
  Faculty Advisor(s): Weitao Chen & Yulong Xing

   

  Samuel Britton
  Dissertation Title: "Mathematical Models of Blood Clot Deformation and Post- Translational Regulation of Enzymes in Metabolic Networks"
  Faculty Advisor(s): Mark Alber

   

  Kenny Courser
  Dissertation Title: "Open Systems: A Double Categorical Perspective"
  Faculty Advisor(s): John C. Baez

   

  Justin Davis
  Dissertation Title: "Generalized Demazure Modules with Level Two Filtrations"
  Faculty Advisor(s): Vyjayanthi Chari

   

  Alexander Henderson
  Dissertation Title: "Fractal Zeta Functions in Metric Spaces"
  Faculty Advisor(s): Michel L.  Lapidus

   

  Dane Lawhorne
  Dissertation Title: "Cluster Structures in Double Canonical Bases"
  Faculty Advisor(s): Jacob Greenstein

   

  Joseph Moeller
  Dissertation Title: "The Grothendieck Construction in Categorical Network Theory"
  Faculty Advisor(s): John C. Baez

   

  Lawrence Mouille
  Dissertation Title: "Positive Intermediate Ricci Curvature with Symmetries"
  Faculty Advisor(s): Frederick Wilhelm

   

  Kevin Tsai
  Dissertation Title: "Computational Study of Cellular Budding at Different Physical Length Scales"
  Faculty Advisor(s): Mark Alber

   

  Adam Yassine
  Dissertation Title: "Generalized Span Categories in Classical Mechanics and the Functoriality of the Legendre Transformation"
  Faculty Advisor(s): Michel L. Lapidus & David E. Weisbart

• 2019 Graduates

  Mikahl Banwarth-Kuhn
  Dissertation Title: "Mathematical Model for Studying Combined Effect of Individual Cell Behavior on Developing Tissue Shape in Plants  "
  Faculty Advisor(s): Mark Alber

   

  Joshua Buli
  Dissertation Title: "Discontinuous Galerkin Methods for Hyperbolic Systems of PDEs and the Bathtub Model for Traffic Flow"
  Faculty Advisor(s): Yulong Xing

   

  Bryan Carrillo
  Dissertation Title: " Vanishing of Certain Axially-Symmetric Periodic D-Solutions to the Stationary Navier-Stokes Equations "
  Faculty Advisor(s): Qi S. Zhang

   

  Daniel Cicala
  Dissertation Title: "Rewriting Structured Cospans: A Syntax for Open Systems"
  Faculty Advisor(s): John C. Baez

   

  Frank Kloster
  Dissertation Title: "Greens Functions On PCF Self-Similar Sets"
  Faculty Advisor(s): Michel L. Lapidus

   

  Christina Knox
  Dissertation Title: "Inverse Problems on Electrical Networks and in Photoacoustic Tomography"
  Faculty Advisor(s): Amir Moradi Fam

   

  Timothy McEldowney
  Dissertation Title: "Strongly Hilbert Modules"
  Faculty Advisor(s): Mei-Chu Chang

   

  Ryan Moruzzi Jr
  Dissertation Title: "Isomorphism of Modules for Type Dn"
  Faculty Advisor(s): Vyjayanthi Chari

   

  Dylan Noack
  Dissertation Title: "A Characterization of Certain Bounded, Convex Domains"
  Faculty Advisor(s): Bun Wong

   

  Xavier Ramos Olive
  Dissertation Title: "Gradient Estimates Under Integral Curvature Conditions"
  Faculty Advisor(s): Qi Zhang

   

  Edward Voskanian
  Dissertation Title: "On the Quasiperiodic Structure of the Complex Dimensions of Self-Similar Fractal Strings"
  Faculty Advisor(s): Michel L. Lapidus

• 2018 Graduates

  Andrea Arauza
  Dissertation Title: "Spectral Triples and Fractal Geometry"
  Faculty Advisor(s): Michel L. Lapidus

   

  Daniel Chun
  Dissertation Title: "Asymptotic Syzygies of Normal Crossing Varieties"
  Faculty Advisor(s): Ziv Ran

   

  Brandon Coya
  Dissertation Title: "Circuits, Bond Graphs, and Signal-Flow Diagrams: A Categorical Perspective"
  Faculty Advisor(s): John C. Baez

   

  Matthew Lee
  Dissertation Title: "Global Weyl Modules and Maximal Parabolics of Twisted Affine Lie Algebras"
  Faculty Advisor(s): Vyjayanthi Chari

   

  Kayla Murray
  Dissertation Title: "Graded Representations of Current Algebras"
  Faculty Advisor(s): Vyjayanthi Chari

   

  James Ogaja
  Dissertation Title: "Function Theory on Open Kahler Manifolds"
  Faculty Advisor(s): Bun Wong

   

  Lauren Ruth
  Dissertation Title: "Two New Settings for Examples of von Neumann Dimension"
  Faculty Advisor(s): Alain Valette & Feng Xu

   

  Alex Sherbetjian
  Dissertation Title: "Rigidification of Algebras Over Algebraic Theories in Diagram Categories"
  Faculty Advisor(s): John C. Baez & Julia E. Bergner

   

  John Simanyi
  Dissertation Title: "The Poisson Cohomology of k-step Nilmanifolds"
  Faculty Advisor(s): Yat S. Poon

   

  Jordan Tousignant, 
  Dissertation Title: "Koszulity of Directed Graded k-linear Categories and Their Quadratic Dual"
  Faculty Advisor(s): Wee L. Gan

• 2017 Graduates

  Jesse Benavides
  Dissertation Title: "New Examples of Collapse With a Lower Curvature Bound"
  Faculty Advisor(s): Frederick Wilhelm

   

  Donna Blanton
  Dissertation Title: "On Tensor Products of Demazure Modules for sl2[t]"
  Faculty Advisor(s): Vyjayanthi Chari

   

  Kyle Castro
  Dissertation Title: "Multiplicative Character Sums and the Applications to Problems in Analytic Number Theory"
  Faculty Advisor(s): Mei-Chu Chang

   

  Hyun Choi
  Dissertation Title: "Semistar Operations on Integral Domains and Multiplicative Lattices"
  Faculty Advisor(s): David E. Rush

   

  Matthew O'Dell
  Dissertation Title: "Integrable Representations for Equivariant Map Algebras Associated with Borel-de Siebenthal Pairs"
  Faculty Advisor(s): Vyjayanthi Chari

   

  Priyanka Rajan
  Dissertation Title: "Geometry and Topology of Some Fake Projective Spaces"
  Faculty Advisor(s): Frederick Wilhelm

   

  Scott Roby
  Dissertation Title: "α-Scaling Zeta Functions For Self-Similar Multifractals"
  Faculty Advisor(s): Michel L. Lapidus

   

  Andrew Walker
  Dissertation Title: "On a Notion of Cohen-Macaulay and the Non-Vanishing of Čech Cohomology Modules"
  Faculty Advisor(s): David E. Rush

   

  Sean Watson
  Dissertation Title: "Fractal Zeta Functions: To Ahlfors Spaces and Beyond"
  Faculty Advisor(s): Michel L. Lapidus

   

  Parker Williams
  Dissertation Title: "Information Gathering on Bounded Degree Trees and Properties of Random Matrices"
  Faculty Advisor(s): Kevin Costello

• 2016 Graduates

  Timothy Cobler
  Dissertation Title: "The Derivative Operator on Weighted Bergman Spaces and Quantized Number Theory"
  Faculty Advisor(s): Michel L. Lapidus

   

  Jason Erbele
  Dissertation Title: "Categories in Control: Applied PROPs"
  Faculty Advisor(s): John C. Baez

   

  Kaylee Hamann
  Dissertation Title: "On the Characterization of Convex Domains With Non-Compact Automorphism Group"
  Faculty Advisor(s): Bun Wong

   

  Joshua Strong
  Dissertation Title: "Boundary Characterization of Iterated Automorphism Orbits on Bounded Domains"
  Faculty Advisor(s): Bun Wong

   

  John Watterlond
  Dissertation Title: "Representation Stability of Consistent Sequences of GL(n, Fq)-Modules"
  Faculty Advisor(s): Wee L. Gan

   

  Robert Willett
  Dissertation Title: "Volume Comparison, Ricci Curvature, and Focal Radius"
  Faculty Advisor(s): Frederick Wilhelm

• 2015 Graduates

  John Dusel
  Dissertation Title: "Combinatorics of Crystal Folding"
  Faculty Advisor(s): Jacob Greenstein

   

  Mathew Lunde
  Dissertation Title: "Self-Extensions and Prime Factorizations of Quantum Affine Algebras"
  Faculty Advisor(s): Vyjayanthi Chari

   

  Esteban Navas
  Dissertation Title: "A Priori Bound on the Velocity in Axially Symmetric Navier Stokes Equations"
  Faculty Advisor(s): Qi S. Zhang

   

  Jason Park
  Dissertation Title: "Random Measure Algebras Under Convolution"
  Faculty Advisor(s): Malempati Rao

   

  Soheil Safii
  Dissertation Title: "Equivariant and Isovariant Function Spaces"
  Faculty Advisor(s): Reinhard Schultz

   

  Lisa Schneider
  Dissertation Title: "Multiplicities Associated to Demazure Flags of sl2[t]-Modules"
  Faculty Advisor(s): Vyjayanthi Chari

   

  Peri Shereen
  Dissertation Title: "A Steinberg Type Decomposition Theorem for Higher Level Demazure Modules"
  Faculty Advisor(s): Vyjayanthi Chari

   

  Jeffrey Wand
  Dissertation Title: "Demazure Flags of Local Weyl Modules"
  Faculty Advisor(s): Vyjayanthi Chari

   

  Jacob West
  Dissertation Title: "Higher Auslander-Reiten Theory"
  Faculty Advisor(s): Julia E. Bergner & Wee L. Gan

• 2014 Graduates

  Chunghoon Kim
  Dissertation Title: "Deformations of Compact Holomorphic Poisson Manifolds and Algebraic Poisson Schemes"
  Faculty Advisor(s): Ziv Ran

   

  Daniel Majcherek
  Dissertation Title: "Multiplicative Lattice Versions of Some Results From Neotherian Commutative Rings"
  Faculty Advisor(s): David E. Rush

   

  Oliver Thistlethwaite
  Dissertation Title: "Seiberg-Witten Invariants, Alexander Polynomials, and Fibred Classes"
  Faculty Advisor(s): Stefano G. Vidussi

• 2013 Graduates

  Dennis Gumaer
  Dissertation Title: "A Jacobi Field Splitting Theorem for Positive Curvature"
  Faculty Advisor(s): Frederick Wilhelm

   

  Matthew Highfield
  Dissertation Title: "Twisted Graded Hecke Algebras for Elementary Abelian Groups"
  Faculty Advisor(s): Wee L. Gan

   

  John Quinn
  Dissertation Title: "Scale Covariance of Fractal Sets and Measures, A Differential Approach to the Box-Counting Function of a Fractal, with Applications"
  Faculty Advisor(s): Michel L.  Lapidus

• 2012 Graduates

  Matthew Bennett
  Dissertation Title: "Tilting Modules for the Current Algebra Associated to a Simple Lie Algebra"
  Faculty Advisor(s): Vyjayanthi Chari

   

  Christopher Carlson
  Dissertation Title: "Foliations, Contract Structures and Finite Group Actions"
  Faculty Advisor(s): Reinhard Schultz

   

  Barbara Herzog
  Dissertation Title: "Sub-Index for Critical Points of Distance Functions"
  Faculty Advisor(s): Frederick Wilhelm

   

  Adam Katz
  Dissertation Title: "Poincare-Birkhoff-Witt Bases for Dioperads"
  Faculty Advisor(s): Wee L. Gan

   

  Nishu Lal
  Dissertation Title: "Spectral Zeta Functions of Laplacians on Self-Similar Fractals"
  Faculty Advisor(s): Michel L. Lapidus

   

  Kwangwoo Lee
  Dissertation Title: "Transfer Theorems on Tautological Modules of Hilbert Schemes of Nodal Curves and de Jonquieres' Formulas"
  Faculty Advisor(s): Ziv Ran

   

  Nathaniael Manning
  Dissertation Title: "Global Weyl Modules for Twisted and Untwisted Loop Algebras"
  Faculty Advisor(s): Vyjayanthi Chari

   

  Robert Niemeyer
  Dissertation Title: "An Investigation of the Koch Snowflake Fractal Billiard: Experimental and Theoretical Results"
  Faculty Advisor(s): Michel L. Lapidus

   

  Paul Oeser
  Dissertation Title: "Monoidal Extensions of a Locally Quasi-Unmixed Unique Factorization Domain"
  Faculty Advisor(s): David E. Rush

   

  Curtis Pro
  Dissertation Title: "On Riemannian Submersions and Diffeomorphism Stability"
  Faculty Advisor(s): Frederick Wilhelm

   

  Michael Sill
  Dissertation Title: "Average Distance Functions and Their Applications"
  Faculty Advisor(s): Frederick Wilhelm

   

  Bradley Thomas
  Dissertation Title: "Boundary Characterization of a Smooth Domain With Non-Compact Automorphism Group"
  Faculty Advisor(s): Bun Wong

   

  Juan Zaragoza
  Dissertation Title: "Orthogonal Partial Conformal Change"
  Faculty Advisor(s): Frederick Wilhelm

• 2011 Graduates

  Jack Bennett
  Dissertation Title: "Some Results on Factorization in Integral Domains"
  Faculty Advisor(s): David E. Rush

   

  Samuel Chamberlin
  Dissertation Title: "Integral Bases for the Universal Enveloping Algebras of Map Algebras"
  Faculty Advisor(s): Vyjayanthi Chari

   

  Hafedh Herichi
  Dissertation Title: "Generalized Fractal Strings, Complex Dimensions and a Spectral Reformulation of the Riemann Hypothesis"
  Faculty Advisor(s): Michel L. Lapidus

   

  John Huerta
  Dissertation Title: "Division Algebras, Supersymmetry and Higher Gauge Theory"
  Faculty Advisor(s): John C. Baez

   

  Azadeh Rafizadeh
  Dissertation Title: "Using Twisted Alexander Polynomials to Detect Fiberability"
  Faculty Advisor(s): Stefano G. Vidussi

   

  Christopher Rogers
  Dissertation Title: "Higher Symplectic Geometry"
  Faculty Advisor(s): John C. Baez

   

  Brian Rolle
  Dissertation Title: "Construction of Weak Mirror Pairs by Deformations"
  Faculty Advisor(s): Yat S. Poon

   

  Christopher Walker
  Dissertation Title: "A Categorification of Hall Algebras"
  Faculty Advisor(s): John C. Baez

• 2010 Graduates

  Ronald Dolbin
  Dissertation Title: "Abelian Subalgebras in Z2-graded Lie Algebras; Partitions, Young Diagrams and Ballot Numbers"
  Faculty Advisor(s): Vyjayanthi Chari

   

  Richard Han
  Dissertation Title: "A Construction of the "2221" Planar Algebra"
  Faculty Advisor(s): Feng Xu

   

  Alexander Hoffnung
  Dissertation Title: "Foundations of Categorified Representation Theory"
  Faculty Advisor(s): John C. Baez

   

  Jennifer Loftus
  Dissertation Title: "Gaussian Bounds of an Equation Derived From the Navier-Stokes Equations"
  Faculty Advisor(s): Qi S. Zhang

   

  Timothy Ridenour
  Dissertation Title: "Faces of Weight Polytopes, a Generalization of a Theorem of Vinberg and Koszul Algebras"
  Faculty Advisor(s): Vyjayanthi Chari

   

  Jonathan Sarhad
  Dissertation Title: "Part I: Spectral Geometry of the Harmonic Gasket; Part II: Nonlinear Poisson Equation via a Newton-Embedding Procedure"
  Faculty Advisor(s): Michel L. Lapidus

• 2009 Graduates

  Vicente Alvarez
  Dissertation Title: "A Numerical Computation of Eigenfunctions for the Kusuoka Laplacian on the Sierpinski Gasket"
  Faculty Advisor(s): Michel L. Lapidus

   

  Scot Childress
  Dissertation Title: "Quantum Measures, Arithmetic Coils, and Generalized Fractal Strings"
  Faculty Advisor(s): Michel L. Lapidus

   

  Shilong Kuang
  Dissertation Title: "Analysis of Conjugate Heat Equation on Complete Non-Compact Riemannian Manifolds Under Ricci Flow"
  Faculty Advisor(s): Qi S. Zhang

   

  Hwa Lee
  Dissertation Title: "The Flag Hilbert Scheme of Points of Nodal Curves and the Punctual Hilbert Scheme of Points of the Cusp Curve"
  Faculty Advisor(s): Ziv Ran

   

  Chau Wong
  Dissertation Title: "On a Class of Commuting Squares"
  Faculty Advisor(s): Masako Asaeda & Feng Xu

• 2008 Graduates

  James Davenport
  Dissertation Title: "Solvability of Some Inhomogeneous Parabolic Equations"
  Faculty Advisor(s): Qi S. Zhang

   

  Peter McLoughlin
  Dissertation Title: "When is the Adjoint of a Finite-Rank Minimal Projection Also Minimal"
  Faculty Advisor(s): Bruce L. Chalmers

   

  Tiffany Troutman
  Dissertation Title: "Infinity-Harmonic Functions, Maps, and Morphisms of Riemannian Manifolds"
  Faculty Advisor(s): Frederick Wilhelm

   

  Chui Yao
  Dissertation Title: "Discrete Logarithm and Related Problems in Cryptography"
  Faculty Advisor(s): Mei-Chu Chang

• 2007 Graduates

  Britta Daudert
  Dissertation Title: "Random Walk on Networks: An Investigation of 1) Localization Phenomena on Fractal Drums 2) The Spread of an Epidemic Throughout a Social Network"
  Faculty Advisor(s): Michel L. Lapidus

   

  Hung Lu
  Dissertation Title: "p-adic Fractal Strings and Their Complex Dimensions"
  Faculty Advisor(s): Michel L. Lapidus

   

  Jeffrey Morton
  Dissertation Title: "Extended TQFT's and Quantum Gravity"
  Faculty Advisor(s): John C. Baez

   

  John Rock
  Dissertation Title: "Zeta Functions, Complex Dimensions of Fractal Strings and Multifractal Analysis of Mass Distributions"
  Faculty Advisor(s): Michel L. Lapidus

   

  Jagannatha Senesi
  Dissertation Title: "Finite-Dimensional Representations of Twisted Loop Algebras"
  Faculty Advisor(s): Vyjayanthi Chari

   

  Derek Wise
  Dissertation Title: "Topological Gauge Theory, Cartan Geometry, and Gravity"
  Faculty Advisor(s): John C. Baez

• 2006 Graduates

  Tobias Bartels
  Dissertation Title: "Higher Gauge Theory: 2-Bundles"
  Faculty Advisor(s): John C. Baez

   

  Catherine Crockett
  Dissertation Title: "On the Topology, Combinatorics, and Geometry of Circle and Spherical Orders"
  Faculty Advisor(s): Stefano G. Vidussi

   

  Lisa Hernandez
  Dissertation Title: "On the Girth of a Knot"
  Faculty Advisor(s): Xiao-Song Lin

   

  Erin Pearse
  Dissertation Title: "Complex Dimensions of Self-Similar Systems"
  Faculty Advisor(s): Michel L. Lapidus

• 2005 Graduates

  Jae-Wook Chung
  Dissertation Title: "The Algebraic Structure of n-Punctured Ball Tangles"
  Faculty Advisor(s): Xiao-Song Lin

   

  Dustin Culhan
  Dissertation Title: "Associated Primes and Primal Decomposition in Modules and Lattice Modules, and Their Duals"
  Faculty Advisor(s): David E. Rush

   

  Eric Overholser
  Dissertation Title: "Boundary Behavior of a Infinitesimal Metric and Intrinsic Measure on Domains and Moduli Space"
  Faculty Advisor(s): Bun Wong

• 2004 Graduates

  Miguel Carrion Alvarez
  Dissertation Title: "Loop Quantization Versus Fock Quantization of p-Form Electromegnetism on Static Spacetimes"
  Faculty Advisor(s): John C. Baez

   

  Alissa Crans
  Dissertation Title: "Lie 2-Algebras"
  Faculty Advisor(s): John C. Baez

   

  Suzanne Lindborg
  Dissertation Title: "Representations of Affine Lie Algebras of Level Zero"
  Faculty Advisor(s): Vyjayanthi Chari

   

  Jianjun Tian
  Dissertation Title: "Evolution Algebras and Evolution Processes on Graphs"
  Faculty Advisor(s): Xiao-Song Lin

• 2003 Graduates

  Dimitar Grantcharov
  Dissertation Title: "Weight Modules of Lie Superalgebras of Type I"
  Faculty Advisor(s): Ivan B. Penkov

   

  Colin Maclaughlin
  Dissertation Title: "Integrable and Abelian Deformations of Abelian Complex Structures on 2-Step Nilmanifolds"
  Faculty Advisor(s): Yat S. Poon

   

  Chanwoo Pae
  Dissertation Title: "Groebner Bases of Veronese Embeddings and N-p Problems"
  Faculty Advisor(s): Mei-Chu Chang

• 2002 Graduates

  Thang Le
  Dissertation Title: "Representations of Infinite Dimensional Lie Algebras"
  Faculty Advisor(s): Vyjayanthi Chari

• 2001 Graduates

  Cyrill Oseledets
  Dissertation Title: "Root Direct Limits of Lie Superalgebras"
  Faculty Advisor(s): Ivan B. Penkov

• 1999 Graduates

  Youngook Choi
  Dissertation Title: "Enumerative Geometry of Plane Curves"
  Faculty Advisor(s): Ziv Ran

   

  Zhiwen Li
  Dissertation Titles: "Rapid Recovery from Link Failure" & "Burau Representation for String Links"
  Faculty Advisor(s): Mart Molle & Xiao-Song Lin

   

  Jonathan Ruyle
  Dissertation Title: "Cardinal Sequences of PCF Structures"
  Faculty Advisor(s): Matthew Foreman & Albert R. Stralka

• 1998 Graduates

  Ivan Dimitrov
  Dissertation Title: "Weight Modules of Infinite-Dimensional Lie Algebras and Lie Superalgebras"
  Faculty Advisor(s): Ivan B. Penkov

   

  Tammy Fisher-Vasta
  Dissertation Title: "Presentations of Z-forms for the Universal Enveloping Algebras of Affine Lie Algebras"
  Faculty Advisor(s): Vyjayanthi Chari

   

  Lillian Kinkade
  Dissertation Title: "Elementary Divisor Rings and Bezout Domains"
  Faculty Advisor(s): David E. Rush

   

  Jaime Londono
  Dissertation Title: "Parametric Estimation of Diffusion Processes Sampled at First Exit Times"
  Faculty Advisor(s): Neil Gretsky

   

  John Noga
  Dissertation Title: "Competitive Analysis of On-Line Algorithms for Paging"
  Faculty Advisor(s): Marek Chrobak

   

  Joseph Vasta
  Dissertation Title: "The Maximum Rank Ideal Problem on the Orthogonal Product of Simplices"
  Faculty Advisor(s): Lawrence H. Harper

   

  Laura Wallace
  Dissertation Title: "Graded Mori Rings"
  Faculty Advisor(s): David E. Rush

• 1997 Graduates

  Ching-Jung Guu
  Dissertation Title: "The Circular Wirelength Problem for Hypercubes"
  Faculty Advisor(s): Lawrence H. Harper

   

  Laurel Langford
  Dissertation Title: "2-Tangles as a Free Braided Monnidal 2-Category with Duals"
  Faculty Advisor(s): John C. Baez

   

  Gwoho Liu
  Dissertation Title: "Application of a Construction of Universal Deformation of a Curve to Schottky Problem"
  Faculty Advisor(s): Ziv Ran

   

  Sara Mohanty
  Dissertation Title: "First Degree Invariants of Almost Generic Plane Immersed Curves"
  Faculty Advisor(s): Oleg Viro

   

  Vladimir Tchernov
  Dissertation Title: "Vassiliev Invariants of Degree One of Knots and Links in R1- and S1- Fibrations"
  Faculty Advisor(s): Oleg Viro

   

  Lih-Chung Wang
  Dissertation Title: "Divisors on Generic Hypersurfaces"
  Faculty Advisor(s): Ziv Ran

• 1996 Graduates

  James Gilliam
  Dissertation Title: "Lagrangian and Symplectic Techniques in Discrete Mechanics"
  Faculty Advisor(s): John C. Baez

   

  Cheryl Griffith
  Dissertation Title: "Numerical Computation and Computer Visualization of the Eigenfunctions for the Koch Snowflake Drum"
  Faculty Advisor(s): Michel L. Lapidus

   

  Qi He
  Dissertation Title: "Generalized Minkowski Content, Vibrations Fractal Drums, Fractal Strings and the Riemann Zeta-Function"
  Faculty Advisor(s): Michel L. Lapidus

   

  Lior Kadosh
  Dissertation Title: "Topics in Weyl Geometry"
  Faculty Advisor(s): Yat S. Poon

   

  Heroe Soedjak
  Dissertation Title: "Asymptotic Properties of Bispectral Density Estimators of Harmonizable Processes"
  Faculty Advisor(s): Malempati M. Rao

• 1995 Graduates

  Michael Green
  Dissertation Title: "Multiparameter Semimartingale Integrals and Boundedness Principles"
  Faculty Advisor(s): Malempati M. Rao

• 1994 Graduates

  Jonathan Fisher
  Dissertation Title: N/A
  Faculty Advisor(s): N/A

   

  Zhongdao Ren
  Dissertation Title: N/A
  Faculty Advisor(s): N/A

   

  Timothy Watson
  Dissertation Title: N/A
  Faculty Advisor(s): N/A

• 1993 Graduates

  Da Chen 
  Dissertation Title: "Kernel Coefficient Ideals" 
  Faculty Advisor(s): Louis J. Ratliff 

   

  Martha Contreras 
  Dissertation Title: "Resonance and Double Resonance for Quasilinear Elliptic Higher Order Partial Differential Equations between the First and Second Eigenvalue" 
  Faculty Advisor(s): Victor L. Shapiro 

   

  Mary Legner 
  Dissertation Title: "Quasilinear Elliptic and Parabolic Partial Differential Equations with a Derivative Driving Force" 
  Faculty Advisor(s): Victor L. Shapiro 

   

  Michael Prophet 
  Dissertation Title: "Codimension One Minimal Projections onto the Quadratics and Their Adjoints" 
  Faculty Advisor(s): Bruce L. Chalmers 

• 1992 Graduates

  Sung Ahn
  Dissertation Title: Asymptotic Primes and Grade Functions
  Faculty Advisor(s): David Rush

   

  Joseph Allen
  Dissertation Title: Curvature of Intrinsic Measures on Complex Manifolds
  Faculty Advisor(s): Bun Wong

   

  Ann Forkeotes
  Dissertation Title: Lattices of Lower Finite Breadth
  Faculty Advisor(s): Gerhard Gierz

   

  Frank Shaw
  Dissertation Title: Discontinuity in Codimension-K Manifold Decompositions
  Faculty Advisor(s): J. Walsh

   

  Randall Swift
  Dissertation Title: Structural and Sample Path Analyses of Harmonizable Random Fields
  Faculty Advisor(s): Ayala Rao

   

  Kazuchika Ushijima
  Dissertation Title: A Ring Representing a Finite Projective Geometry
  Faculty Advisor(s): David Rush

• 1991 Graduates

  Shawnee McMurran
  Dissertation Title: N/A
  Faculty Advisor(s): N/A

• 1990 Graduates

  Marc Mehlman
  Dissertation Title: Moving Average Representations and PRediction for Multidimensional Strongly Harmonizable Processes
  Faculty Advisor(s): M. M. Rao

• 1989 Graduates

  Tarik Bourezgue
  Dissertation Title: Completely NonBoundary Normal Operators in Finitely Connected Domains
  Faculty Advisor(s): James Stafney

• 1988 Graduates

  Rebecca Michaelis
  Dissertation Title: Straight Sublattice of Euclidean Space
  Faculty Advisor(s): Albert Stralka

• 1987 Graduates

  Joseph Chavez
  Dissertation Title: A Natural Notion of Morphism for Linear Programming Problems
  Faculty Advisor(s): Lawrence Harper

   

  Joseph Sroka
  Dissertation Title:  pNA Games Through Infinite-Dimensional Banach Spaces
  Faculty Advisor(s): Neil Gretsky

• 1986 Graduates

  John Fay
  Dissertation Title: Second and Higher Order Quasilinear Ellipticity on the N-torus
  Faculty Advisor(s): Victor Shapiro

   

  Gary Griffing
  Dissertation Title:  Cofree Lie and Other Coalgebras
  Faculty Advisor(s): Richard E. Block

   

  Fowzi Sejeeni
  Dissertation Title: Best Approximation in C(T)-Modules
  Faculty Advisor(s): Gerhard Gierz

• 1984 Graduates

  Saadat Moussavi
  Dissertation Title: Generalized Two Parametric "SOR" Method for Linear Sparse Systems
  Faculty Advisor(s): John de Pillis

   

  Barbara Shabell
  Dissertation Title: Computable Error Estimates Resulting from Modifications of Newton's Method for Finding Roots
  Faculty Advisor(s): Fred Metcalf

• 1983 Graduates

  Hosien Moghadam
  Dissertation Title: Compression Operators and a Solution to the Bandwidth Problem of the Product of n Paths
  Faculty Advisor(s): Lawrence Harper

   

  Derek Chang
  Dissertation Title: Bimeasures, Harmonizable Processes and Filtering
  Faculty Advisor(s): M. M. Rao

   

  Gary Palosaari
  Dissertation Title: Spectral Decomposition for Non-selfadjoint Perturbations of Singular Bessel Differential Operators
  Faculty Advisor(s): James Stafney

   

  Bradley Parsons
  Dissertation Title: N/A
  Faculty Advisor(s): N/A

• 1982 Graduates

  Melody Duncan
  Dissertation Title: Order Dimension in Compact Partially Ordered Spaces
  Faculty Advisor(s): Albert Stralka

   

  Juana Iroz
  Dissertation Title: Associated Primes, Attached Primes and Cograde
  Faculty Advisor(s): David Rush

   

  David Motte
  Dissertation Title: A Constructive Approach to Minimal Projections in Banach Spaces
  Faculty Advisor(s): Bruce Chalmers