Here you can find information on past Ph.D. graduates such as dissertation, advisor, employer and position as well as information on past M.S. and M.A. graduates such as thesis and advisor.

For questions or page updates please fill out the form below.

Please note the information regarding employer and position is subject to change and may not be completely up to date.

#### August 2024

- Denny, Bud. An Unstructured Mesh Coordinate Transformation Based FDTD Method. Advisor: Moysey Brio. Employer: Air Force Research Laboratory. Position: Computational Scientist.
- Dirdak, Abigayle. The Gale Transform and the Pentagram Map. Advisor: Anton Izosimov. Employer: College of the Sequoias. Position: Adjunct Professor.
- Koc, Tugce. Supervised Learning by Low Rank Estimation on Tensor Data. Advisor: Hao Zhang.
- Lewis, Daniel. Newton Slopes of Specializations. Advisor: Bryden Cais.
- Loomis, Alexandre. MIW Sequences. Advisor: Sunder Sethuraman.
- Sidbury, Lee. Convergence of Discrete Conformal Maps of Surfaces. Advisor: David Glickenstein.

#### May 2024

- Guzman, Anthony. Reductions of Some Crystalline Representations in the Unramified Setting. Advisors: Brandon Levin and Bryden Cais.
- Hand, Leaha. Difference Operators and Pentagram Maps Over Rings. Advisor: Anton Izosimov.
- Ledesma Granados, Jorge. Trivial Source Character Tables of Sporadic Groups. Advisor: Klaus Lux.
- Roon, Eric. Two Spatial Correlation Estimates in Quantum Statistical Mechanics. Advisor: Robert Sims. Employer: Michigan State University. Position: Visiting Assistant Professor.
- Wei, Bolun. L-Functions for a Family of Generalized Kloosterman Sums in Two Variables. Advisor: C. Douglas Haessig.

#### August 2023

- Banks, Robert. Improving PL Approximations of Harmonic Maps and a Penalty-Function Approach to Harmonic Maps. Advisor: David Glickenstein. Employer: University of Arizona, Tucson AZ. Position: Instructor.
- Doehrman, Thomas. Spaces of Spheres, Duality Structures, and the Finite Volume Laplacian. Advisor: David Glickenstein. Employer: University of Arizona, Tucson AZ. Position: Instructor.
- Knak, Rachel. Kisin Varieties Associated to Redicuble Galois Representations of Dimension 2. Advisor: Brandon Levine.
- Nelson, Spencer. On the Arithmetic Gan-Gross-Prasad Conjecture for U(2) x U(3). Advisor: Hang Xue.

#### May 2023

- Phillips, Tristan. Counting Rational Points of Bounded Height on Some Genus Zero Modular Curves. Advisor: Bryden Cais. Employer: Dartmoth College, Hanover, NH. Position: NSF Postdoctoral Researcher.

#### December 2022

- Rios, Jocelyn. Crticially Examining the Multilingual Undergraduate Mathematics Classroom: A

Mixed Methods Study. Advisors: Marta Civil and Adi Adiredja.

#### August 2022

- Agrawal, Utkarsh. Central Values of Degree Six L-Functions: The Case of Hilbert Modular Forms. Advisor: Hang Xue. Employer: Ben-Gurion University of the Negev, Beer Sheva, Israel. Position: Postdoctoral Researcher.
- Elert, Eric. Algorithms for Finite Dimensional Algebras Over Finite Fields using Basic Algebras. Advisor: Klaus Lux. Employer: Savannah College of Art and Design, Savannah, GA. Position: Math Professor.
- Latifi Jebelli, Mohammad Javed. Loop Group Factorization, Lattice Systems and OPUC. Advisor: Douglas Pickrell. Employer: Dartmouth College, Hanover, NH. Position: Postdoctoral Researcher.
- Wu, Ruiyang. New Dimension Reduction Methods for Quadratic Discriminant Analysis. Advisor: Ning Hao. Employer: New York University School of Global Public Health, New York, NY. Postdoctoral Researcher.

#### May 2022

- Priver, Kyle. Generalizing Bondal-Orlov Criteria for Deligne-Mumford Stacks. Advisor: Jack Hall

#### August 2021

- Kaushish, Madhav. Theory Building in Geometry Education: Developing and Implementing a Course for 12 to 15 Year Old Students. Advisor: Rebecca McGraw
- Kling, Anthony. Comparison of Integral Structures on the Space Modular Forms of Full Level. Advisor: Bryden Cais.

#### December 2020

- Biegel, Hannah. Near Real-Time Forecasting of Epidemics Using Data Assimilation with Simple Models. Advisor: Joceline Lega. Employer: SomaLogic. Position: Scientist I- Bioinfomatics.
- Luo, Zhaorui (Jerry). Probabilistic Graphical Model Inference and Learning in Crowdsourcing and Turbulence. Advisor: Junming Yin. Employer: Google, Mountain View, CA. Position: Data Scientist.

#### August 2020

- Quinones, Jason. Mathematical Aspects of Gauge Theory: Nahm's Equations and Jacobi Forms. Advisor: Christoph Keller. Employer: Gallaudet University, Washington. D.C. Position: Assistant Professor.
- Ramalheira-Tsu, Jonathan. The Kostant-Toda Lattice, Combinatorial Algorithms and Ultra-Discrete Dynamics. Advisor: Nicholas Ercolani. Employer: University of Arizona, Tucson, AZ. Position: Visiting Assistant Professor.

#### May 2020

- Coatney, Ryan. A Responsibile Softmax Layer in Deep Learning. Advisor: Marek Rychlik. Employer: Brevium. Position: Data Scientist.
- Hoskins, Philip. Analytical and Numerical Study of Inverse Problems Arising in Some Novel Imaging Modalities. Advisor: Leonid Kunyansky. Employer: Raytheon, Tucson, AZ. Position: Senior Systems Engineer.
- Lunderman, Spencer. Feature-Based Parameter Estimation of the Nonlinear Cloud and Rain Equation and Global Bayesian Optimization in Data Assimilation. Advisor: Matthias Morzfeld. Employer: CIT Bank, Pasadna CA. Position: Independent Model Validation.
- Oliver, Rachel. Superiority of Bayes Estimators Over the MLE in High Dimensional Models on Compact Riemannian Manifolds and its Implication for Nonparametric Bayes. Advisor: Rabindra Bhattacharya. Employer: Rincon Research Corporation, Tucson AZ. Position: Research Scientist.
- Taylor, J. David. Extending Oda's Theorem to Curves with Ordinary Singularities. Advisor: Bryden Cais.
- Tippings, Brandon. Discrete Painlevé Equations, Orthogonal Polynomials, and Counting Maps. Advisor: Nicholas Ercolani. Employer: Clothing Tech LLC. Austin, TX. Position: Software Developer.

#### August 2019

- Dai, Yan. Mirror Model and Critical Percolation. Advisor: Tom Kennedy. Employer: Jacksonville University, Jacksonville, FL. Position: Assistant Professor.
- Lippitt, William. Clumping, Stick-breaking, and an Inhomogeneous Markov Chain. Advisor: Sunder Sethuraman. Employer: University of Arizona, Tucson, AZ. Position: Visiting Assistant Professor.
- Murphy, Dylan. Additions for Jacobi Operators and the Toda Hierarchy of Lattice Equations. Advisor: Nicholas Ercolani. Employer: University of Arizona, Tucson AZ. Position: Lecturer, School of Information.

#### May 2019

- Fang, Lanbo. Eigenvalue Asymptotics of Narrow Domains. Advisor: Leonid Friedlander.

#### January 2019

- Tao, Yuan. The Potential Exterior to Close-to-touching Discs. Advisor: Shankar Venkataramani. Employer: Ventana Medical Systems. Position: Biostatistician.

#### December 2018

- Gonzalez, Angelica. Spectral Properties of 3-Regular Graphs Related to One-Face Maps. Advisor: Nicholas Ercolani. Employer: Raytheon. Position: Engineer.
- MacLaughlin, Andrew. Using Homogeneous Structures to Measure Homogeneity of Riemannian Manifolds. Advisor: David Glickenstein. Employer: Raytheon. Position: Engineer
- Moussa, Mohamad. Beyond Raid 6 — Efficient Error Correcting Code for Dual-Disk Corruption. Advisor: Marek Rychlik. Employer: American Express. Position: Senior Engineer.
- Tsinnajinnie, Belin. Indigenous and Latinx Students' Developing Mathematical Identities. Advisor: Marta Civil. Employer: Santa Fe Community College. Position: Assistant Professor and Co-Chair in Mathematics.

#### August 2018

- Fox, Matthew. Spectrum of Random Hamiltonian Matrices. Advisor: Nicholas Ercolani. Employer: Raytheon. Position: Senior Engineer, Signal Processing.
- Liang, Jinjin. Curvature Flows on Polygons and Surface Clusters. Advisor: David Glickenstein. Employer: Wells Fargo Bank N.A. Position: Quantitative Associate.
- Wang, Jun. Invariants of Modular Curves and Sharifi's Conjectures. Advisors: Bryden Cais, Romyar Sharifi. Employer: University of British Columbia. Position: Postdoctoral Researcher, Department of Mathematics.

#### May 2018

- Gunton, Cody. Torsion 1-Crystalline Representations and Néron Component Groups in the Semi-stable Case. Advisor: Bryden Cais. Employer: University of Copenhagen, Copenhagen, Denmark. Position: Postdoctoral Researcher, Department of Mathematics.
- Pounder, Kyle. Nearly Singular Jacobi Matrices and Applications to the Finite Toda Lattice. Advisor: Nicholas Ercolani. Employer: Emailage, Chandler, AZ. Position: Fraud Decision Scientist.
- Rossi, Daniel. Fields of Values in Finite Groups: Characters and Conjugacy Classes. Advisor: Pham H. Tiep. Employer: SUNY Binghamton, Binghamton, NY. Position: Visiting Assistant Professor.
- Shahar, Doron. Hydrodynamic limits for long range asymmetric processes and probabilistic opinion dynamics. Sunder Sethuraman.
- Shih, Sheng-Chi. On Congruence Modules Related To Hilbert Eisenstein Series. Advisors: Bryden Cais, Romyar Sharifi. Employer: University of Lille 1. Position: Postdoctoral Researcher, Department of Mathematics.

#### December 2017

- Stone, Megan. Eigenvalue Densities for the Hermitian Two-Matrix Model and Connections to Monotone Hurwitz Numbers. Advisor: Nicholas Ercolani.

#### May 2017

- Lee, Hyereem. Triples in Finite Groups and a Conjecture of Guralnick and Tiep. Advisor: Pham H. Tiep. Employer: Samsung Insurance, Seoul, Korea. Position: JP.
- Zhelezov, Gleb. Coalescing Particle Systems. Applications to Nonlinear Fokker-Planck Equations. Advisor: Ibrahim Fatkullin. Employer:Case Western Reserve University, Cleveland, OH. Position: Postdoctoral Researcher, Department of Biology.

#### August 2016

- Berard, Whitney. Explicit Serre Weight Conjectures in Dimension Four. Advisor: David Savitt. Employer: Mills College, Oakland, CA. Position: Adjunct Assistant Professor.
- Brown, Tova. Asymptotics and Dynamics of Map Enumeration Problems. Advisor: Nicholas Ercolani. Current participant in the Program on Combinatorics and Interactions, Institut Henri Poincare, Marseille/Paris.
- Davis, Erik. Consistency of Modularity Clustering on Random Geometric Graphs. Advisor: Sunder Sethuraman. Employer: University of Arizona, Tucson, AZ. Position: Postdoctoral Fellow.
- Trefethen, Stephen. Non-abelian Composition Factors of m-Rational Groups. Advisor: Pham Huu Tiep. Employer: The College of William and Mary, Williamsburg, VA. Position: Visiting Assistant Professor.
- Williams, Ronnie Scott. Level Compatibility in the Passage from Modular Symbols to Cup Products. Advisor: Romyar Sharifi. Employer: The University of Central Oklahoma,Edmond, OK. Position: Assistant Professor.

#### May 2016

- Henniges, Alex. Kisin-Ren Classification of Pi-divisible O-modules via the Dieudonné Crystal. Advisor: Bryden Cais. Employer: Raytheon. Position: Sr. Software Engineer.
- Ma, Ding. Relations Among Multiple Zeta Values and Modular Forms of Low Level. Advisor: Romyar Sharifi. Employer: Duke University, Durham, NC. Position: Postdoctoral Research Associate.

#### August 2015

- Chavez, Angel. Werner's Measure on Self-Avoiding Loops and Representations of the Virasoro Algebra. Advisor: Douglas Pickrell. Employer: Pomona College. Position: Postdoctoral Fellow.
- Thomas, Joseph. Conformal Variations of Piecewise Constant Curvature Two and Three Manifolds. Advisor: David Glickenstein. Employer: ViaSat Inc. Position: Data Scientist/Software Engineer.

#### May 2015

- Jiang, Jianping. Random Walks and their Scaling Limits. Advisor: Thomas Kennedy. Employer: NYU Shanghai. Position: Postdoctoral Fellow.
- Lafferty, Matthew J. Eichler-Shimura Cohomology Groups and the Iwasawa Main Conjecture. Advisor: Romyar Sharifi. Employer: University of California, Los Angeles. Position: Adjunct Assistant Professor.
- Powell, Kevin J. Modular Symbols Modulo Eisenstein Ideals for Bianchi Spaces. Advisor: Romyar Sharifi. Employer: Snow College. Position: Assistant Professor.
- Todd, George E. Linear Relations between Multizeta Values. Advisor: Klaus Lux. Employer: Union College. Position: Visiting Assistant Professor of Mathematics.
- Waters, Patrick T. Combinatorics of the Hermitian 1-Matrix Model. Advisor: Nicholas Ercolani. Employer: Temple University. Position: Research Assistant Professor.

#### December 2014

- Blackburn, Chantel C. Mathematics According to Whom? Two Elementary Teachers and Their Encounters with the Mathematical Horizon. Advisor: Rebecca McGraw. Employer: Pacific Union College. Position: Assistant Professor of Mathematics.
- Hinkel, Dustin E. Constructing Simultaneous Diophantine Approximations of Certain Cubic Numbers. Advisor: Marek Rychlik.

#### August 2014

- Maienschein, Thomas D. Desingularizing the boundary of the moduli space of genus one stable quotients. Advisor: Yi Hu. Employer: Drake University. Position: Visiting Assistant Professor.
- Prasad, Priya V. Connection, motivation, & alignment: Exploring the effects of content-based mathematics professional development. Advisor: Rebecca McGraw. Employer:University of Texas, San Antonio. Position: Assistant Professor.

#### August 2024

• Juricic, Nicholas. Advisor: Marta Civil.

• Roberts, Jeremy. Advisor: Christopher Henderson.

• Serdarevic, Haris. Advisor: Serin Hong.

#### May 2024

• Arreguin, Joseph**. *** Girsanov's Theorem: Measure Theoretic Transformations of Stochastic Integrals. *Advisor: Ibrahim Fatukullin

• Roberts, Ashley**.** Advisor: Christopher Henderson.

#### May 2023

• Ruchi Dahiya. Title unknown. Advisor: Ibrahim Fatukullin.

#### December 2022

• Jorge Ledesma Granados. Title unknown. Advisor: Klaus Lux.

• Lee Sidbury. Title unknown. Advisor: David Glickenstein.

#### August 2022

• Conner Hatton.* Gambler's Ruin: The Limiting Distribution of Points Visited Exactly Once of a Simple Random Walk up to Time of Exit and the Influencer Voter Model. *Advisor: Sunder Sethuraman.

#### May 2022

- Owen MacDonald.
*Almost Sure Convergence of Adjacent Weights in a Preferential Attachment Random Graph.*Advisor: Sunder Sethuraman.

#### December 2021

- Abigayle Dirdak.
*The Gale Transform*. Advisor: Anton Izosimov.

#### August 2021

- Omer Aktepe.
*Discontinuous Galerkin Methods For One And Two Dimensional Schrodinger Equations*. Advisor: Moysey Brio. - Bud Denny.
*Extended Finite-Difference Time-Domain Method for Dynamics in Ferrite Material*. Advisor: Moysey Brio.

#### May 2021

- Florence Dungan.
*A Nonparametric Test for Equality of Distributions*. Advisor: Kevin Lin. - Justin Perkins-Ollila.
*Image Quality Improvement in Generative Adversarial Nets using the Structural Similarity Index Measure*. Advisor: Helen Zhang.

#### May 2020

- Brian Bennett.
*An Exploration of Parent-Child Conversations at a Mathematics Exhibit*. Advisor: Marta Civil. - Chloe Ondracek. Title unknown. Advisor: Robert Sims.
- Fany Salazar.
*Mathematical Conversations with Mexican Mothers: Why Teachers Should Care*. Advisor: Marta Civil.

#### December 2019

- Madhav Kuashish.
*Assumption Digging in Euclidean Geometry*. Advisor: Rebecca McGraw. - Alyssa Turnquist.
*What Mathematics Graduate Teaching Assistants Value in a Professional Development Program*. Advisor: Marta Civil.

#### May 2019

- Angela Kraft. Title unknown. Advisor: Klaus Lux.

#### May 2018

- Hannah Biegel. Title unknown. Advisor: Joceline Lega.

#### December 2016

- Arias Hathaway Turner.
*Understanding Reform: A Study of the Standards Movement in Mathematics Education.*Advisor: Marta Civil.

#### August 2016

- Amy Been.
*Teaching Views of Mathematical Modeling*. Advisor: Marta Civil.

#### May 2015

- Rachel Baumann. Title unknown. Advisor: Klaus Lux.
- Angelica Gonzalez. Title unknown. Advisor: Nick Ercolani.

#### May 2014

- Jonathan Edwards.
*Commentary on Explicit Calculations of the Zeta Function-Regularized Determinant of the Laplacian on the n-sphere*. Advisor: Douglas Pickrell. - Michael Phizicky. Title unknown. Advisor: Sunder Sethuraman.