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Department of Mathematics

College of Natural & Agricultural Sciences

Our Ph.D. Graduates

Year Dissertation Title Author Faculty Advisor(s)
2025 Representation Stability of Motzkin Algebras Dan Bayleran Wee L. Gan
2025 Fractal Cohomology of the Ternary Cantor Set, Light Condensed Fractal Cohomology, and Fractal Descent Shanna Dobson Michel L. Lapidus
2025 Metric Deformations and Intermediate Ricci Curvature Hasan M. El-Hasan Frederick Wilhelm
2025 A Multiscale Model on Hair Follicle Bulb Replenishment and Concentric Layered Differentiation Mingye Gao Qixuan Wang
2025 Compact Moduli Spaces of Marked Plane Curves Aaron Goodwin Patricio Gallardo Candela
2025 Multiscale Modeling of Cell Migration in Biological Systems Austin P. Hansen Mark Alber, Heyrim Cho
2025 Multiscale Modeling of CAR T-Cell Treatment for Heterogeneous Glioblastoma Tony Li Heyrim Cho, Qixuan Wang
2025 Stated Skein Theory and Double Affine Hecke Algebra Representations Raymond A. Matson Peter Samuelson
2025 Brownian Motion In Zp is a Limit of Discrete Time Random Walks Tyler J. Pierce David E. Weisbart
2025 Multi-Scale Mathematical Modeling Study of Proper Shape Formation During Epithelial Tissue Development Jennifer Rangel Ambriz Mark Alber
2025 Equivalent Conditions for Domination Of M(2,C)-Sequences Chang Sun Zhenghe Zhang
2025 A Numerical Investigation of the Beam Equation with Power- Law Materials and a Model of Tissue Growth in Arabidopsis Isaac J. Tate Weitao Chen
2025 The Curtain Model of CAT(0) Spaces and its Relationship to the Sublinearly Morse Boundary Elliott Vest Matthew Durham
2025 Generalized Demazure Modules for the Twisted Current Algebra 2A ̃2l−1 Joseph P. Wagner Vyjayanthi Chari
2024 New Classes of Moving Anchor Extragradient James Alcala Yat Tin Chow
2024 Mathematical Modeling of Hair Follicle Regeneration Cecilia Duran Qixuan Wang, Weitao Chen
2024 Conicality of Morse Limit Sets and Stability Jacob Garcia Matthew Durham
2024 Representations of FI-Like Categories Associated to Anthony Muljat Wee Liang Gan
2024 Fractional Taylor Series Expansions for Classes of Matthew Overduin Michel Lapidus
2024 Striated Regularity of Vorticity in a Bounded Domain Thomas Schellhous James Kelliher
2024 Multiscale Models for Developing Tissues or Organs in Alysha Toomey Weitao Chen, Mark Alber
2024 A Characterization of Bounded Convex Domains in C^n with Non-Compact Automorphism Group Gabrielle Tsai Bun Wong
2022 Information Gathering Problem in Ad-Hoc Radio Networks With Layer Topology Gefei Chen Kevin Costello
2022 Avoiding Monochromatic Solutions to Linear Equations Gabriel Elvin Kevin Costello
2021 Representation Theory for Oriented Matroids and Combinatorial Intersection Homology for Gorenstein* Meet- Semilattices Ethan Kowalenko Carl Mautner
2021 Stability of Current Density Impedance Imaging and Uniqueness for the Inverse Sturm-Liouville Problem Robert Lopez Amir Moradi Fam
2021 Representations of Some Categories of FI Type Derek Lowenberg Wee Gan
2021 Boundary Asymptotics for Convex and Strongly Pseudoconvex Domains Alexander Martin Bun Wong
2021 Composing Behaviors of Networks Jade Master John C. Baez
2021 Dubrovnik Skein Theory and Power Sum Elements Alexander Pokorny Peter Samuelson
2020 Solutions to the 2D Euler Equations Satisfying the Serfati Condition With Relaxed Constraints on the Initial Vorticity Taylor Baldwin James P. Kelliher
2020 High Order Numerical Methods for Hyperbolic Balance Laws: Well-Balanced Discontinuous Galerkin Methods and Adjoint- Based Inverse Algorithms Jolene Britton Weitao Chen & Yulong Xing
2020 Mathematical Models of Blood Clot Deformation and Post- Translational Regulation of Enzymes in Metabolic Networks Samuel Britton Mark Alber
2020 Open Systems: A Double Categorical Perspective Kenny Courser John C. Baez
2020 Generalized Demazure Modules with Level Two Filtrations Justin Davis Vyjayanthi Chari
2020 Fractal Zeta Functions in Metric Spaces Alexander Henderson Michel L. Lapidus
2020 Cluster Structures in Double Canonical Bases Dane Lawhorne Jacob Greenstein
2020 The Grothendieck Construction in Categorical Network Theory Joseph Moeller John C. Baez
2020 Positive Intermediate Ricci Curvature with Symmetries Lawrence Mouille Frederick Wilhelm
2020 Computational Study of Cellular Budding at Different Physical Length Scales Kevin Tsai Mark Alber
2020 Generalized Span Categories in Classical Mechanics and the Functoriality of the Legendre Transformation Adam Yassine Michel L. Lapidus & David E. Weisbart
2019 Mathematical Model for Studying Combined Effect of Individual Cell Behavior on Developing Tissue Shape in Plants Mikahl Banwarth-Kuhn Mark Alber
2019 Discontinuous Galerkin Methods for Hyperbolic Systems of PDEs and the Bathtub Model for Traffic Flow Joshua Buli Yulong Xing
2019 Vanishing of Certain Axially-Symmetric Periodic D-Solutions to the Stationary Navier-Stokes Equations Bryan Carrillo Qi S. Zhang
2019 Rewriting Structured Cospans: A Syntax for Open Systems Daniel Cicala John C. Baez
2019 Greens Functions On PCF Self-Similar Sets Frank Kloster Michel L. Lapidus
2019 Inverse Problems on Electrical Networks and in Photoacoustic Tomography Christina Knox Amir Moradi Fam
2019 Strongly Hilbert Modules Timothy McEldowney Mei-Chu Chang
2019 Isomorphism of Modules for Type Dn Ryan Moruzzi Jr Vyjayanthi Chari
2019 A Characterization of Certain Bounded, Convex Domains Dylan Noack Bun Wong
2019 Gradient Estimates Under Integral Curvature Conditions Xavier Ramos Olive Qi Zhang
2019 On the Quasiperiodic Structure of the Complex Dimensions of Self-Similar Fractal Strings Edward Voskanian Michel L. Lapidus
2018 Spectral Triples and Fractal Geometry Andrea Arauza Michel L. Lapidus
2018 Asymptotic Syzygies of Normal Crossing Varieties Daniel Chun Ziv Ran
2018 Circuits, Bond Graphs, and Signal-Flow Diagrams: A Categorical Perspective Brandon Coya John C. Baez
2018 Global Weyl Modules and Maximal Parabolics of Twisted Affine Lie Algebras Matthew Lee Vyjayanthi Chari
2018 Graded Representations of Current Algebras Kayla Murray Vyjayanthi Chari
2018 Function Theory on Open Kahler Manifolds James Ogaja Bun Wong
2018 Two New Settings for Examples of von Neumann Dimension Lauren Ruth Alain Valette & Feng Xu
2018 Rigidification of Algebras Over Algebraic Theories in Diagram Categories Alex Sherbetjian John C. Baez & Julia E. Bergner
2018 The Poisson Cohomology of k-step Nilmanifolds John Simanyi Yat S. Poon
2018 Koszulity of Directed Graded k-linear Categories and Their Quadratic Dual Jordan Tousignant, Wee L. Gan
2017 New Examples of Collapse With a Lower Curvature Bound Jesse Benavides Frederick Wilhelm
2017 On Tensor Products of Demazure Modules for sl2[t] Donna Blanton Vyjayanthi Chari
2017 Multiplicative Character Sums and the Applications to Problems in Analytic Number Theory Kyle Castro Mei-Chu Chang
2017 Semistar Operations on Integral Domains and Multiplicative Lattices Hyun Choi David E. Rush
2017 Integrable Representations for Equivariant Map Algebras Associated with Borel-de Siebenthal Pairs Matthew O'Dell Vyjayanthi Chari
2017 Geometry and Topology of Some Fake Projective Spaces Priyanka Rajan Frederick Wilhelm
2017 α-Scaling Zeta Functions For Self-Similar Multifractals Scott Roby Michel L. Lapidus
2017 On a Notion of Cohen-Macaulay and the Non-Vanishing of Čech Cohomology Modules Andrew Walker David E. Rush
2017 Fractal Zeta Functions: To Ahlfors Spaces and Beyond Sean Watson Michel L. Lapidus
2017 Information Gathering on Bounded Degree Trees and Properties of Random Matrices Parker Williams Kevin Costello
2016 The Derivative Operator on Weighted Bergman Spaces and Quantized Number Theory Timothy Cobler Michel L. Lapidus
2016 Categories in Control: Applied PROPs Jason Erbele John C. Baez
2016 On the Characterization of Convex Domains With Non-Compact Automorphism Group Kaylee Hamann Bun Wong
2016 Boundary Characterization of Iterated Automorphism Orbits on Bounded Domains Joshua Strong Bun Wong
2016 Representation Stability of Consistent Sequences of GL(n, Fq)-Modules John Watterlond Wee L. Gan
2016 Volume Comparison, Ricci Curvature, and Focal Radius Robert Willett Frederick Wilhelm
2015 Combinatorics of Crystal Folding John Dusel Jacob Greenstein
2015 Self-Extensions and Prime Factorizations of Quantum Affine Algebras Mathew Lunde Vyjayanthi Chari
2015 A Priori Bound on the Velocity in Axially Symmetric Navier Stokes Equations Esteban Navas Qi S. Zhang
2015 Random Measure Algebras Under Convolution Jason Park Malempati Rao
2015 Equivariant and Isovariant Function Spaces Soheil Safii Reinhard Schultz
2015 Multiplicities Associated to Demazure Flags of sl2[t]-Modules Lisa Schneider Vyjayanthi Chari
2015 A Steinberg Type Decomposition Theorem for Higher Level Demazure Modules Peri Shereen Vyjayanthi Chari
2015 Demazure Flags of Local Weyl Modules Jeffrey Wand Vyjayanthi Chari
2015 Higher Auslander-Reiten Theory Jacob West Julia E. Bergner & Wee L. Gan
2014 Deformations of Compact Holomorphic Poisson Manifolds and Algebraic Poisson Schemes Chunghoon Kim Ziv Ran
2014 Multiplicative Lattice Versions of Some Results From Neotherian Commutative Rings Daniel Majcherek David E. Rush
2014 Seiberg-Witten Invariants, Alexander Polynomials, and Fibred Classes Oliver Thistlethwaite Stefano G. Vidussi
2013 A Jacobi Field Splitting Theorem for Positive Curvature Dennis Gumaer Frederick Wilhelm
2013 Twisted Graded Hecke Algebras for Elementary Abelian Groups Matthew Highfield Wee L. Gan
2013 Scale Covariance of Fractal Sets and Measures, A Differential Approach to the Box-Counting Function of a Fractal, with Applications John Quinn Michel L. Lapidus
2012 Tilting Modules for the Current Algebra Associated to a Simple Lie Algebra Matthew Bennett Vyjayanthi Chari
2012 Foliations, Contract Structures and Finite Group Actions Christopher Carlson Reinhard Schultz
2012 Sub-Index for Critical Points of Distance Functions Barbara Herzog Frederick Wilhelm
2012 Poincare-Birkhoff-Witt Bases for Dioperads Adam Katz Wee L. Gan
2012 Spectral Zeta Functions of Laplacians on Self-Similar Fractals Nishu Lal Michel L. Lapidus
2012 Transfer Theorems on Tautological Modules of Hilbert Schemes of Nodal Curves and de Jonquieres' Formulas Kwangwoo Lee Ziv Ran
2012 Global Weyl Modules for Twisted and Untwisted Loop Algebras Nathaniael Manning Vyjayanthi Chari
2012 An Investigation of the Koch Snowflake Fractal Billiard: Experimental and Theoretical Results Robert Niemeyer Michel L. Lapidus
2012 Monoidal Extensions of a Locally Quasi-Unmixed Unique Factorization Domain Paul Oeser David E. Rush
2012 On Riemannian Submersions and Diffeomorphism Stability Curtis Pro Frederick Wilhelm
2012 Average Distance Functions and Their Applications Michael Sill Frederick Wilhelm
2012 Boundary Characterization of a Smooth Domain With Non-Compact Automorphism Group Bradley Thomas Bun Wong
2012 Orthogonal Partial Conformal Change Juan Zaragoza Frederick Wilhelm
2011 Some Results on Factorization in Integral Domains Jack Bennett David E. Rush
2011 Integral Bases for the Universal Enveloping Algebras of Map Algebras Samuel Chamberlin Vyjayanthi Chari
2011 Generalized Fractal Strings, Complex Dimensions and a Spectral Reformulation of the Riemann Hypothesis Hafedh Herichi Michel L. Lapidus
2011 Division Algebras, Supersymmetry and Higher Gauge Theory John Huerta John C. Baez
2011 Using Twisted Alexander Polynomials to Detect Fiberability Azadeh Rafizadeh Stefano G. Vidussi
2011 Higher Symplectic Geometry Christopher Rogers John C. Baez
2011 Construction of Weak Mirror Pairs by Deformations Brian Rolle Yat S. Poon
2011 A Categorification of Hall Algebras Christopher Walker John C. Baez
2010 Abelian Subalgebras in Z2-graded Lie Algebras; Partitions, Young Diagrams and Ballot Numbers Ronald Dolbin Vyjayanthi Chari
2010 A Construction of the "2221" Planar Algebra Richard Han Feng Xu
2010 Foundations of Categorified Representation Theory Alexander Hoffnung John C. Baez
2010 Gaussian Bounds of an Equation Derived From the Navier-Stokes Equations Jennifer Loftus Qi S. Zhang
2010 Faces of Weight Polytopes, a Generalization of a Theorem of Vinberg and Koszul Algebras Timothy Ridenour Vyjayanthi Chari
2010 Part I: Spectral Geometry of the Harmonic Gasket; Part II: Nonlinear Poisson Equation via a Newton-Embedding Procedure Jonathan Sarhad Michel L. Lapidus
2009 A Numerical Computation of Eigenfunctions for the Kusuoka Laplacian on the Sierpinski Gasket Vicente Alvarez Michel L. Lapidus
2009 Quantum Measures, Arithmetic Coils, and Generalized Fractal Strings Scot Childress Michel L. Lapidus
2009 Analysis of Conjugate Heat Equation on Complete Non-Compact Riemannian Manifolds Under Ricci Flow Shilong Kuang Qi S. Zhang
2009 The Flag Hilbert Scheme of Points of Nodal Curves and the Punctual Hilbert Scheme of Points of the Cusp Curve Hwa Lee Ziv Ran
2009 On a Class of Commuting Squares Chau Wong Masako Asaeda & Feng Xu
2008 Solvability of Some Inhomogeneous Parabolic Equations James Davenport Qi S. Zhang
2008 When is the Adjoint of a Finite-Rank Minimal Projection Also Minimal Peter McLoughlin Bruce L. Chalmers
2008 Infinity-Harmonic Functions, Maps, and Morphisms of Riemannian Manifolds Tiffany Troutman Frederick Wilhelm
2008 Discrete Logarithm and Related Problems in Cryptography Chui Yao Mei-Chu Chang
2007 Random Walk on Networks: An Investigation of 1) Localization Phenomena on Fractal Drums 2) The Spread of an Epidemic Throughout a Social Network Britta Daudert Michel L. Lapidus
2007 p-adic Fractal Strings and Their Complex Dimensions Hung Lu Michel L. Lapidus
2007 Extended TQFT's and Quantum Gravity Jeffrey Morton John C. Baez
2007 Zeta Functions, Complex Dimensions of Fractal Strings and Multifractal Analysis of Mass Distributions John Rock Michel L. Lapidus
2007 Finite-Dimensional Representations of Twisted Loop Algebras Jagannatha Senesi Vyjayanthi Chari
2007 Topological Gauge Theory, Cartan Geometry, and Gravity Derek Wise John C. Baez
2006 Higher Gauge Theory: 2-Bundles Tobias Bartels John C. Baez
2006 On the Topology, Combinatorics, and Geometry of Circle and Spherical Orders Catherine Crockett Stefano G. Vidussi
2006 On the Girth of a Knot Lisa Hernandez Xiao-Song Lin
2006 Complex Dimensions of Self-Similar Systems Erin Pearse Michel L. Lapidus
2005 The Algebraic Structure of n-Punctured Ball Tangles Jae-Wook Chung Xiao-Song Lin
2005 Associated Primes and Primal Decomposition in Modules and Lattice Modules, and Their Duals Dustin Culhan David E. Rush
2005 Boundary Behavior of a Infinitesimal Metric and Intrinsic Measure on Domains and Moduli Space Eric Overholser Bun Wong
2004 Loop Quantization Versus Fock Quantization of p-Form Electromegnetism on Static Spacetimes Miguel Carrion Alvarez John C. Baez
2004 Lie 2-Algebras Alissa Crans John C. Baez
2004 Representations of Affine Lie Algebras of Level Zero Suzanne Lindborg Vyjayanthi Chari
2004 Evolution Algebras and Evolution Processes on Graphs Jianjun Tian Xiao-Song Lin
2003 Weight Modules of Lie Superalgebras of Type I Dimitar Grantcharov Ivan B. Penkov
2003 Integrable and Abelian Deformations of Abelian Complex Structures on 2-Step Nilmanifolds Colin Maclaughlin Yat S. Poon
2003 Groebner Bases of Veronese Embeddings and N-p Problems Chanwoo Pae Mei-Chu Chang
2002 Representations of Infinite Dimensional Lie Algebras Thang Le Vyjayanthi Chari
2001 Root Direct Limits of Lie Superalgebras Cyrill Oseledets Ivan B. Penkov
1999 Enumerative Geometry of Plane Curves Youngook Choi Ziv Ran
1999   Zhiwen Li Mart Molle & Xiao-Song Lin
1999 Cardinal Sequences of PCF Structures Jonathan Ruyle Matthew Foreman & Albert R. Stralka
1998 Weight Modules of Infinite-Dimensional Lie Algebras and Lie Superalgebras Ivan Dimitrov Ivan B. Penkov
1998 Presentations of Z-forms for the Universal Enveloping Algebras of Affine Lie Algebras Tammy Fisher-Vasta Vyjayanthi Chari
1998 Elementary Divisor Rings and Bezout Domains Lillian Kinkade David E. Rush
1998 Parametric Estimation of Diffusion Processes Sampled at First Exit Times Jaime Londono Neil Gretsky
1998 Competitive Analysis of On-Line Algorithms for Paging John Noga Marek Chrobak
1998 The Maximum Rank Ideal Problem on the Orthogonal Product of Simplices Joseph Vasta Lawrence H. Harper
1998 Graded Mori Rings Laura Wallace David E. Rush
1997 The Circular Wirelength Problem for Hypercubes Ching-Jung Guu Lawrence H. Harper
1997 2-Tangles as a Free Braided Monnidal 2-Category with Duals Laurel Langford John C. Baez
1997 Application of a Construction of Universal Deformation of a Curve to Schottky Problem Gwoho Liu Ziv Ran
1997 First Degree Invariants of Almost Generic Plane Immersed Curves Sara Mohanty Oleg Viro
1997 Vassiliev Invariants of Degree One of Knots and Links in R1- and S1- Fibrations Vladimir Tchernov Oleg Viro
1997 Divisors on Generic Hypersurfaces Lih-Chung Wang Ziv Ran
1996 Lagrangian and Symplectic Techniques in Discrete Mechanics James Gilliam John C. Baez
1996 Numerical Computation and Computer Visualization of the Eigenfunctions for the Koch Snowflake Drum Cheryl Griffith Michel L. Lapidus
1996 Generalized Minkowski Content, Vibrations Fractal Drums, Fractal Strings and the Riemann Zeta-Function Qi He Michel L. Lapidus
1996 Topics in Weyl Geometry Lior Kadosh Yat S. Poon
1996 Asymptotic Properties of Bispectral Density Estimators of Harmonizable Processes Heroe Soedjak Malempati M. Rao
1995 Multiparameter Semimartingale Integrals and Boundedness Principles Michael Green Malempati M. Rao
1994 N/A Jonathan Fisher N/A
1994 N/A Zhongdao Ren N/A
1994 N/A Timothy Watson N/A
1993 Kernel Coefficient Ideals Da Chen Louis J. Ratliff
1993 Resonance and Double Resonance for Quasilinear Elliptic Higher Order Partial Differential Equations between the First and Second Eigenvalue Martha Contreras Victor L. Shapiro
1993 Quasilinear Elliptic and Parabolic Partial Differential Equations with a Derivative Driving Force Mary Legner Victor L. Shapiro
1993 Codimension One Minimal Projections onto the Quadratics and Their Adjoints Michael Prophet Bruce L. Chalmers
1992 Asymptotic Primes and Grade Functions Sung Ahn David Rush
1992 Curvature of Intrinsic Measures on Complex Manifolds Joseph Allen Bun Wong
1992 Lattices of Lower Finite Breadth Ann Forkeotes Gerhard Gierz
1992 Discontinuity in Codimension-K Manifold Decompositions Frank Shaw J. Walsh
1992 Structural and Sample Path Analyses of Harmonizable Random Fields Randall Swift Ayala Rao
1992 A Ring Representing a Finite Projective Geometry Kazuchika Ushijima David Rush
1991 N/A Shawnee McMurran N/A
1990 Moving Average Representations and PRediction for Multidimensional Strongly Harmonizable Processes Marc Mehlman M. M. Rao
1989 Completely NonBoundary Normal Operators in Finitely Connected Domains Tarik Bourezgue James Stafney
1988 Straight Sublattice of Euclidean Space Rebecca Michaelis Albert Stralka
1987 A Natural Notion of Morphism for Linear Programming Problems Joseph Chavez Lawrence Harper
1987 pNA Games Through Infinite-Dimensional Banach Spaces Joseph Sroka Neil Gretsky
1986 Second and Higher Order Quasilinear Ellipticity on the N-torus John Fay Victor Shapiro
1986 Cofree Lie and Other Coalgebras Gary Griffing Richard E. Block
1986 Best Approximation in C(T)-Modules Fowzi Sejeeni Gerhard Gierz
1984 Generalized Two Parametric "SOR" Method for Linear Sparse Systems Saadat Moussavi John de Pillis
1984 Computable Error Estimates Resulting from Modifications of Newton's Method for Finding Roots Barbara Shabell Fred Metcalf
1983 Compression Operators and a Solution to the Bandwidth Problem of the Product of n Paths Hosien Moghadam Lawrence Harper
1983 Bimeasures, Harmonizable Processes and Filtering Derek Chang M. M. Rao
1983 Spectral Decomposition for Non-selfadjoint Perturbations of Singular Bessel Differential Operators Gary Palosaari James Stafney
1983 N/A Bradley Parsons N/A
1982 Order Dimension in Compact Partially Ordered Spaces Melody Duncan Albert Stralka
1982 Associated Primes, Attached Primes and Cograde Juana Iroz David Rush
1982 A Constructive Approach to Minimal Projections in Banach Spaces David Motte Bruce Chalmers
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