Our Ph.D. Graduates

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

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: N/A
Faculty Advisor(s): N/A

Joseph Allen
Dissertation Title: N/A
Faculty Advisor(s): N/A

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: N/A
Faculty Advisor(s): N/A

1991 Graduates

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

1990 Graduates

Marc Mehlman
Dissertation Title: N/A
Faculty Advisor(s): N/A

1989 Graduates