### Dissertations from 2024

Diving Deeper into Supercuspidal Representations, Prerna Agarwal

Higher Order Operator Splitting Schemes with Complex Coefficients and Applications, Arun Banjara

The Modular Generalized Springer Correspondence for the Symplectic Group, Joseph Dorta

Modeling and Numerical Analysis of the Cholesteric Landau-de Gennes Model, Andrew L. Hicks

Asymptotic Formula for Scattering Problems Related to Thin Metasurfaces, Zachary Jermain

Finite Monodromy and Artin Representations, Emma Lien

The Lowest Discriminant Ideal of Cayley-Hamilton Hopf Algebras, Zhongkai Mi

Subroups of Coxeter Groups and Stallings Foldings, Jake A. Murphy

Unavoidable Topological Minors of Large or Infinite 3-connected Rooted Graphs, Phuc A. Nguyen

Analytic Wavefront Sets of Spherical Distributions on the De Sitter Space, Iswarya Sitiraju

Auslander-Reiten Triangles on a Bounded Derived Category of Constructible Complexes, Vishnu Prasad Sivaprasad

Reducibility of Schrödinger Operators on Multilayer Graphs, Jorge Villalobos Alvarado

### Dissertations from 2023

Analytic Continuation of Toeplitz Operators and Commuting Families of C*-Algebras, Khalid Bdarneh

Matroid Generalizations of Some Graph Results, Cameron Crenshaw

Finite Element Methods for Elliptic Optimal Control Problems with General Tracking, SeongHee Jeong

Some New Techniques and their Applications in the Theory of Distributions, Kevin Kellinsky-Gonzalez

SL(2,Z) Representations and 2-Semiregular Modular Categories, Samuel Nathan Wilson

First-Order Algorithms for Nonlinear Structured Optimization, Miao Zhang

### Dissertations from 2022

Unavoidable Structures in Large and Infinite Graphs, Sarah Allred

Connected Sums and Directed Systems in Knot Floer Homologies, Sudipta Ghosh

A Cluster Structure on the Coordinate Ring of Partial Flag Varieties, Fayadh Kadhem

Navier-Stokes equations in one and two dimensions, Jon Nerdal

Bloch Spectra for High Contrast Elastic Media, Jayasinghage Ruchira Nirmali Perera

A New Perspective on a Polynomial Time Knot Polynomial, Robert John Quarles

General Stochastic Calculus and Applications, Pujan Shrestha

Characterizations of Certain Classes of Graphs and Matroids, Jagdeep Singh

Anticipating Stochastic Integrals and Related Linear Stochastic Differential Equations, Sudip Sinha

On a Relation Between ADO and Links-Gould Invariants, Nurdin Takenov

### Dissertations from 2021

Applications of Nonstandard Analysis in Probability and Measure Theory, Irfan Alam

A Conjecture on the Irregularity Function for Local Geometric Langlands Parameters and the Formal Frenkel-Gross Connection, Andrew Alaniz

Rigid Connections on the Projective Line with Elliptic Toral Singularities, Alisina Azhang

Study of Parity Sheaves Arising from Graded Lie Algebras, Tamanna Chatterjee

Accelerated Gradient Descent Methods For the Uniaxially Constrained Landau-de Gennes Model, Edison E. Chukwuemeka

Connectivity of Matroids and Polymatroids, Zachary R. Gershkoff

Stochastic Navier-Stokes Equations with Markov Switching, Po-Han Hsu

An Equivalence Between Contact Gluing Maps in Sutured Floer Homology: A Conjecture of Zarev, Charles Ryan Leigon

On Properties of Weil Sums of Binomials, Liem P. Nguyen

Nonlinear Potential Analysis on Sobolev Multiplier Spaces, Keng Hao Ooi

Congruences Between Coefficients of a Class of Eta-Quotients and their Applications to Combinatorics, Shashika Petta Mestrige

Algorithms Related to Triangle Groups, Bao The Pham

Noncommutative Tensor Triangular Geometry and Its Applications to Representation Theory, Kent Barton Vashaw

### Dissertations from 2020

Some Results on Seymour’s Second-Neighborhood Conjecture and on Decompositions of Graphs, Farid Bouya

Combinatorial and Asymptotic Statistical Properties of Partitions and Unimodal Sequences, Walter McFarland Bridges

On Selected Subclasses of Matroids, Tara Elizabeth Fife

Multigrid Methods for Elliptic Optimal Control Problems, Sijing Liu

### Dissertations from 2019

Design of Metamaterials for Optics, Abiti Adili

Dehn Functions of Bestvina-Brady Groups, Yu-Chan Chang

Reflection Positivity: A Quantum Field Theory Connection, Joseph W. Grenier

Equivalence of Contact Gluing Maps in Sutured Floer Homology, Federico Salmoiraghi

Quantum Cluster Algebras at Roots of Unity, Poisson-Lie Groups, and Discriminants, Kurt Malcolm Trampel III

### Dissertations from 2018

Unavoidable Immersions and Intertwines of Graphs, Matthew Christopher Barnes

Two Results in Drawing Graphs on Surfaces, Joshua E. Fallon

Templates for Representable Matroids, Kevin Manuel Grace

Dimers on Cylinders over Dynkin Diagrams and Cluster Algebras, Maitreyee Chandramohan Kulkarni

Invariant of Noncommutative Algebras and Poisson Geometry, Bach Van Nguyen

Non-local Methods in Fracture Dynamics, Eyad Said

Curve Tracking Control Under State Constraints and Uncertainties, Robert Kelly Sizemore

Mixed Categories of Sheaves on Toric Varieties, Sean Michael Taylor

On Structures of Large Rooted Graphs, Shilin Wang

Spectra of Quantum Trees and Orthogonal Polynomials, Zhaoxia Wang

Backstepping and Sequential Predictors for Control Systems, Jerome Avery Weston

The Graphs and Matroids Whose Only Odd Circuits Are Small, Kristen Nicole Wetzler

Mathematics Course for Elementary Teachers in an Alternate Certification Pathway, Rachael Cramer Williams

### Dissertations from 2017

On Braids, Branched Covers and Transverse Invariants, Jose Hector Ceniceros

Characterizations of Some Classes of Graphs That Are Nearly Series-Parallel, Victoria Fontaine

Asymptotic Formulae for Restricted Unimodal Sequences, Richard Alexander Frnka

On the Skein Theory of 0-framed Surgery Along the Trefoil Knot, Andrew Robert Holmes

Manifestations of Symmetry in Polynomial Link Invariants, Kyle Istvan

Moduli Spaces of Flat GSp-Bundles, Neal David Livesay

Electromagnetic Resonant Scattering in Layered Media with Fabrication Errors, Emily Anne McHenry

Extraction of Displacement Fields in Heterogeneous Media Using Optimal Local Basis Functions, Paul Derek Sinz

Reduced Order Models for Beam-Wave Interaction in High Power Microwave Sources, Lokendra Singh Thakur

### Dissertations from 2016

Dynamic Resonant Scattering of Near-Monochromatic Fields, Gayan Shanaka Abeynanda

Global a priori Estimates and Sharp Existence Results for Quasilinear Equations on Nonsmooth Domains., Karthik Adimurthi

Option Volatility & Arbitrage Opportunities, Mikael Boffetti

A Conditioned Gaussian-Poisson Model for Default Phenomena, Tyler Brannan

Cluster Algebras and Maximal Green Sequences for Closed Surfaces, Eric Bucher

Excluding a Weakly 4-connected Minor, Kimberly Sevin D'souza

Method of the Riemann-Hilbert Problem for the Solution of the Helmholtz Equation in a Semi-infinite Strip, Ashar Ghulam

Twisted Reflection Positivity, Mostafa Ahmad Hayajneh

Properties of Polynomial Identity Quantized Weyl Algebras, Jesse S. F. Levitt

Derived Geometric Satake Equivalence, Springer Correspondence, and Small Representations, Jacob Paul Matherne

Fractal Shapes Generated by Iterated Function Systems, Mary Catherine McKinley

Beyond the Tails of the Colored Jones Polynomial, Jun Peng

On Properties of Matroid Connectivity, Simon Pfeil

Towards Theory and Applications of Generalized Categories to Areas of Type Theory and Categorical Logic, Lucius Traylor Schoenbaum

Evolution Semigroups for Well-Posed, Non-Autonomous Evolution Families, Austin Keith Scirratt

Riemann-Hilbert Formalism in the Study of Crack Propagation in Domains with a Boundary, Aleksandr Smirnov

Spectral Properties of Photonic Crystals: Bloch Waves and Band Gaps, Robert Paul Viator Jr

### Theses from 2015

Exploring Rational Numbers in Middle School, Robyn Jasmin Boudoin

Shape Optimization for Drag Minimization Using the Navier-Stokes Equation, Chukwudi Paul Chukwudozie

Partial Cosine-Funk Transforms at Poles of the Cosine-λ Transform on Grassmann Manifolds, Christopher Adam Cross

Wavelets, Coorbit Theory, and Projective Representations, Amer Hasan Darweesh

A Study of Mathematical Equivalence: The Importance of the Equal Sign, Christy De'sha Duncan

Excluding Two Minors of the Petersen Graph, Adam Beau Ferguson

Analysis of Nonlinear Dispersive Model Equations, Jacob Grey

Knots, Skein Theory and q-Series, Mustafa Hajij

Left-orderability, Cyclic Branched Covers and Representations of the Knot Group, Ying Hu

Well-Quasi-Ordering by the Induced-Minor Relation, Chanun Lewchalermvongs

Topological Dynamics On Compact Phase Spaces, Lieth Abdalateef Majed