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Department of Mathematics

College of Natural & Agricultural Sciences

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

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