**Recent Ph.D. Graduates**

This section gives information about all students who completed Ph.D. degrees in Mathematics since 1992. Data provided are: year of graduation, student's name, dissertation title, advisor, and initial post-doctoral employment (if available), according to our records.

## 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.

## December 2013

- Herrera-Valdez, Marco.Geometry and non-linear dynamics underlying excitability phenotypes in biophysical models of membrane potential. Advisor: Joceline Lega. Employer: National Institute of Public Health, Mexico. Position: Research Scientist.

## August 2013

- Islambekov, Umar. Lieb-Robinson bounds for the Toda lattice. Advisor: Robert Sims. Employer: Department of Mathematics, University of Pittsburgh. Position: Lecturer.
- Gilbert, Michael. Investigating the relationship between restriction measures and self-avoiding walks. Advisor: Thomas Kennedy. Employer: University of Arizona. Position: Instructor
- Leslie, Martin. Hypermap-homology quantum codes. Advisor: Marek Rychlik. Employer: Streamscale.
- Thomas, Matthew. Analyzing Conceptual Gains in Introductory Calculus with Interactively-Engaged Teaching Styles. Advisor: Guadalupe I. Lozano. Employer: Department of Mathematics, University of Central Arkansas. Position: Assistant Professor.

## May 2013

- Acosta, Enrique.
*Leading order asymptotics of a partition function for colored triangulations*. Advisor: Kenneth McLaughlin. Employer: Mathematics Department, Universite Catholique de Louvain, Belgium. Position: Postdoctoral Fellow. - Bishop, Michael.
*Quantum Systems in Bernoulli Potentials*. Advisor: Jan Wehr. Employer: Department of Mathematics, University of California, Davis, Davis, CA. Position: Krener Assistant Professorship. - Hadad, Yaron.
*Integrable Nonlinear Relativistic Equations*. Advisor: Vladimir Zakharov. Employer: Department of Mathematics, Universidad Nacional de Colombia, Medellin, Colombia. Position: Independent Researcher. - Park, Chol.
*Semi-stable deformation rings in Hodge--Tate weights (0,1,2)*. Advisor: David Savitt. Employer: Mathematics Department, The University of Toronto, Toronto, Ontario, Canada. Position: Postdoctoral Fellow. - Schaeffer Fry, Amanda.
*Irreducible Representations of Finite Groups of Lie Type: On the Irreducible Restriction Problem and Some Local-Global Conjectures*. Advisor: Pham H. Tiep. Employer: Department of Mathematics, Michigan State University, East Lansing, MI. Position: Postdoctoral Fellow.

## August 2012

- Nguyen, Dong Quan.
*Nonexistence of rational points on certain varieties*. Advisor: Romyar Sharifi. Employer: University of British Columbia, Vancouver. Position: Postdoctoral Fellow - Smith, Ryan.
*Serre Weights: The Partially Ramified Case*. Advisor: David Savitt.

## May 2012

- Chuan Huang.
*Novel Methods for T2 Estimation Using Highly Undersampled Radial MRI*. Advisor: Qiu-dong Wang. Employer: Harvard Medical School, Department of Radiology, Boston, MA. Position: Poctdoctoral Fellow. - Matthew Johnson. A Classification of all Hecke Eigenform Product Identities. Advisor: Kirti Joshi.
- Lizhen Lin.
*Nonparametric Inference for Bioassay*. Advisor: Rabindra Bhattacharya. Employer: Duke University, Statistical Science Department, Durham, NC. Position: Postdoctoral Associate. - Aleksandar Petrov.
*On A-Expansions on Drinfeld Modular Forms*. Advisor: Dinesh Thakur. Employer: Texas A&M University at Doha, Qatar, Mathematics Department. Position: Postdoctoral Research Associate. - Victor Piercey.
*Resolutions of Collinearity Among Four Points in the Complex Projective Plane*. Advisor: Yi Hu. Employer: Ferris State University, Mathematics Department, Big Rapids, MI. Position: Assistant Professor (tenure-track). - Jordan Schettler.
*The Change in Lambda Invariants for Cyclick p-Extensions of Z_p-fields*. Advisor: William McCallum. Employer: University of California, Mathematics Department, Santa Barbara, CA. Position: Visiting Assistant Professor.

## December 2011

- Yuliya Gorlina.
*Weighted Delaunay triangulations of piecewise-flat surfaces.*Advisor: David Glickenstein.

## May 2011

- Daniel Champion.
*Mobius Structures, Einstein Metrics, and Conformal Variations on Piecewise Flat Two and Three Dimensional Manifolds*. Advisor: David Glickenstein. Employer: Ventana Medical Systems. Position: Consultant. - David Herzog.
*Ergodicity of Certain Degenerate Complex Diffusion Processes*. Advisor: Jan Wehr. Employer: Duke University, Durham, NC. Position: Visiting Assistant Professor.

## December 2010

- Yijun Shao.
*A Compactification of the Space of Algebraic Maps from P^1 to a Grassmannian*. Advisor: Yi Hu. Employer: Wesleyan University, Middletown, CT. Position: Visiting Assistant Professor.

## August 2010

- Jefferson Taft.
*Intrinsic Geometric Flows on Manifolds of Revolution*. Advisor: David Glickenstein. Employer: University of Arizona. Position: Visiting Assistant Professor. - Brad Weir.
*The Transfer of Momentum from Waves to Currents due to Wave Breaking*. Advisor: Juan Restrepo. Employer: College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, OR. Position: Postdoc. - Mei Yin.
*Spectral Properties of the Renormalization Group.*Advisor: William Faris. Employer: University of Texas at Austin, Austin, TX. Position: Bing Instructorship.

## May 2010

- John Kerl.
*Critical behavior for the model of random spatial permutations.*Advisor: Thomas Kennedy. Employer: Two Sigma Investments, New York, NY. Position: Quantitative Software Developer. - Thomas LaGatta.
*Geodesics of Random Riemannian Metrics.*Advisor: Jan Wehr. Employer: Courant Institute of Mathematical Sciences. Position: Postdoc. - Thomas Occhipinti.
*Mordell-Weil Groups of Large Rank in Towers.*Advisor: Douglas Ulmer. Employer: University of California, Irvine. Position: Postdoctoral Visiting Assistant Professor.

## December 2009

- Grethe Hystad.
*Periodic Ising Correlations.*Advisor: John Palmer. Employer: University of Arizona. Position: Adjunct Instructor. - McKenzie Lamb.
*Ginzburg-Weinstein Isomorphisms for Pseudo-Unitary Lie Groups*. Advisor: Philip Foth. Employer: Ripon College. Position: Assistant Professor. - Bridget Kennedy.
*Modeling pulse propagation in loss-compensated materials that exhibit the negative refreactive index property*. Advisor: Ildar Gabitov. Employer: Department of Defense. - Aramian Wasielak.
*Various limiting criteria for multidimensional diffusion processes*. Advisor: Rabindra Bhattacharya. Employer: Lighthouse Financial.

## August 2009

- Joshua Chesler. Interacting with Algebra: Mathematicians, mathematics educators, and teachers making sense of algebra content. Advisor: Rebecca McGraw. Employer: California State University, Long Beach. Position: Assistant Professor.
- Benjamin Dyhr. The Chordal Loewner Equation Driven by Brownian Motion with a Linear Drift. Advisor: Tom Kennedy. Employer: Metropolitan State College of Denver. Position: Visiting Assistant Professor.

## May 2009

- Selin Kalaycioglu. Computing the projective indecomposable modules of large finite groups. Advisor: Klaus Lux. Employer. Kenyon College, Gambier, OH. Position: Visiting Assistant Professor.

## December 2008

- Abhishek Bhattacharya. Nonparametric statistics on manifolds with applications to shape spaces. Advisor: Rabindra Bhattacharya. Employer: Duke University, Durham, NC. Position: Post-doctorate Researcher.

## May 2008

- Cameron McLeman. A Golod-Shafarevich Equality and p-Tower Groups. Advisor: William McCallum. Employer: Willamette University, Salem, OR. Position: Post-doc.

## December 2007

- Milos Ivkovic. Characterization and Coding Techniques for Long-Haul Optical Telecommunication Systems. Advisor: Bane Vasic (ECE). Employer: LSI Logic Corporation, Allentown, PA. Position: Research Scientist.
- Justin Miller. On p-adic Continued Fractions and Quadratic Irrationals. Advisor: Dinesh Thakur. Employer: IBM, Enterprise Storage Performance Department, Tucson, AZ. Position: Staff Firmware Engineer.

## August 2007

- Lisa Berger. Ranks of Abelian Varieties in Towers of Function Fields. Advisor: Douglas Ulmer. Employer: SUNY at Stony Brook. Position: Assistant Professor.
- Anthony Fernandes. Building alliances: A partnership between a middle school mathematics teacher and a university researcher. Advisor: Peter Wiles. Employer: University of North Carolina at Charlotte. Position: Assistant Professor.

## May 2007

- Arlo Caine. Poisson Structures on U/K and Applications. Advisor: Douglas Pickrell. Employer: Max-Planck-Institut fuer Mathematik, Bonn, Germany; Notre Dame. Position: Visiting Scholar; Postdoctoral Fellow.
- Assane Lo. Witten Laplacian Methods for Critical Phenomena.. Advisor: Haru Pinson. Employer: KFUPM (King Fahd University of Petroleum & Minerals), Dhahran, Saudi Arabia. Position: Assistant Professor.
- Predrag Punosevac. Regularization of Simultaneous Binary Collisions in Some Gravitational Systems.. Advisor: Qiu-dong Wang. Employer: The University of Arizona. Position: Adjunct Lecturer.

## August 2006

- Derek Habermas. Compact Symmetric Spaces, Triangular Factorization, and Cayley Coordinates. Advisor: Douglas Pickrell. Employer: State University of New York, Potsdam. Position: Assistant Professor.
- Panagiota Konstantinou. Homomorphisms of the fundamental group of a surface into PSU (1,1), and the action of the mapping class group. Advisor: Douglas Pickrell. Employer: Frederick University, Cyprus. Position: Lecturer.
- Benjamin Levitt. Tate-Shafarevich Groups of Jacobians of Fermat Curves. Advisor: William McCallum. Employer: California State University, Chico. Position: Assistant Professor.
- Adam Spiegler. Stability of generic equilibria of the 2n dimensional free rigid body using the energy-Casimir method. Advisor: Hermann Flaschka. Employer: The University of Arizona. Position: Visiting Assistant Professor.

## May 2006

- Robert Pawloski. Computing the Cohomology Ring and Ext-Algebra of Group Algebras. Advisor: Klaus Lux. Employer: Monmouth University, West Long Branch, NJ. Position: Assistant Professor.

## August 2005

- Jason Belnap. Putting TAs into Context: Understanding the Graduate Mathematics Teaching Assistant. Advisor: Marta Civil. Employer: Brigham Young University. Position: Faculty Position in Mathematics Education.
- Frederick Leitner. Deformation Theory of Noncommutative Formal Groups in Positive Characteristic. Advisor: Minhyong Kim. Employer: Ben Gurion University, Beer Sheva, Israel. Position: Postdoc.

## August 2004

- Guadalupe Lozano. Poisson Geometry of the Ablowitz-Ladik Equations. Advisor: Nicholas Ercolani. Employer: University of Michigan, Ann Arbor, MI. Position: Assistant Professor.
- Alexander Perlis. On the projective geometry of curves of genus one, and an algorithm for the jacobian of such a curve. Advisor: William McCallum. Employer: The University of Arizona Department of Mathematics. Position: Computer System Administration.
- Katrina Piatek-Jimenez. Undergraduate Mathematics Students' Understanding of Mathematical Statements and Proofs. Advisor: Marta Civil. Employer: Mathematics Department, Central Michigan University, Mount Pleasant, MI. Position: Assistant Professor.
- Patrick Shipman. Plant Patterns. Advisor: Alan Newell. Employer: Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany. Position: Postdoc.

## May 2004

- Thomas Hoffman. Constructing Basic Algebras for the Principal Block of Sporadic Simple Groups. Advisor: Klaus Lux. Employer: Department of Applied Mathematics, Coastal Carolina University, Conway, SC. Position: Assistant Professor.
- Virgil Pierce. The Asymptotic Expansion of the Partition Function of Random Matrices. Advisor: Nicholas Ercolani. Employer: Brandeis University, Waltham, MA. Position: Postdoc.
- Christopher Rasmussen. Jacobians of Etale Covers of the Projective Line Minus Three Points. Advisor: Minhyong Kim. Employer: Mathematics Department, Rice University, Houston, TX. Position: G.C. Evans Instructorship.
- Jeffrey Selden. The Density of States in a Quasi-Gap. Advisor: Leonid Friedlander. Employer: Erwin Schroedinger International Institute for Mathematical Physics, Vienna, Austria. Position: Postdoc.
- Aaron Wootton. Defining Algebraic Polynomials for Cyclic Prime Covers of the Riemann Sphere. Advisor: Klaus Lux. Employer: Department of Mathematics, The University of Portland. Position: Assistant Professor.

## 2002

- Fahd Al-Shammari. Jacobians of Plane Quintic Curves of Genus One. Advisor: William McCallum. Employer: King Khalid Academy, Riyadh, Saudi Arabia. Position: Mathematics Assistant Professor.
- Maria Agrotis. Pure and Applied Reflections on the Reduced Maxwell-Bloch System. Advisor: Nicholas Ercolani. Employer: University of Massachusetts, Amherst, MA. Position: Postdoctoral Fellow.
- Jennifer Smith. An Investigation of Undergraduates' Understanding of Congruence of Integers. Advisor: Marta Civil. Employer: University of Texas, Austin. Position: Assistant Professor.

## 2001

- Jeffrey Edmunds. A Study of a Stage-Structured Model of Two Competing Species. Advisor: Jim Cushing. Employer: University of Mary Washington, Fredericksburg, VA. Position: Assistant Professor.
- Seog Young Kim. Vector Bundles on an Elliptic Curve Over a Discrete Valuation Ring. Advisor: Minhyong Kim. Employer: Samsung Insurance Company, Seoul, Korea. Position: Administrative Manager.
- Weiye Li. Stability of Equilibria in Dynamic Oligopolies. Advisors: Marek Rychlik and Ferenc Szidarovsky. Employer: Los Alamos National Laboratory. Position: Postdoctoral Fellow.
- Susan Hammond Marshall. Crystalline Representations and Néron Models. Advisor: Minhyong Kim. Employer: University of Texas, Austin. Position: VIGRE Postdoctoral Fellow.

## 2000

- Geoffrey Cunningham. Sums of Squares in Function Fields of Elliptic Curves. Advisor: Douglas Ulmer. Employer: National Security Agency. Position: Cryptologic Mathematician.
- Jia-Ling Dai. Conjugacy Classes, Characters, and Co-adjoint Orbits of Diff
^{+}(S^{1}). Advisor: Doug Pickrell. Employer: Zhejiang University, Hangzhou, PR China. Position: Instructor. - David Marshall. Galois Groups and Greenberg's Conjecture. Advisor: William McCallum. Employer: McMaster University, Hamilton, Ontario. Position: Postdoctoral Fellow.
- Chunnan Wang. Analysis of a Bivariate Distribution in Reliability Theory. Advisor: Moshe Shaked. Employer: Premera Blue Cross, Seattle, WA. Position: Actuary.

## 1999

- Maref Alzoubi. A Dispersal Model for Structured Populations. Advisor: Jim Cushing. Employer: Yarmouk University, Irbid, Jordan. Position: Instructor.
- Micaela Avila de Brau. Controlled Markov Chains with Exponential Risk-Sensitive Criteria: Modularity, Structured Policies and Applications. Advisor: Emmanuel Fernandez (SIE). Employer: Universidad Nacional Autónoma de México, Hermosillo.
- Agustin Brau Rojas. Controlled Markov Chains with Risk-Sensitive Average Cost Criterion. Advisor: Emmanuel Fernandez (SIE). Employer: Universidad Nacional Autónoma de México, Hermosillo.
- Aaron Ekstrom. On the Infinitude of Elliptic Carmichael Numbers. Advisor: Dinesh Thakur. Employer: Alfred University (NY). Position: Assistant Professor.
- Jack Jackson II. Splitting in Finite Metacyclic Groups. Advisor: Larry Grove. Employer: Westark College, Fort Smith, AR. Position: Instructor.
- Scott Sakamoto. The Cranmer Abacus: Its Use in Teaching Mathematics to Students with Visual Impairments. Advisor: Steve Willoughby. Employer: Chapman University, Orange, CA. Position: Assistant Professor.

## 1998

- Gregory Gillis. Design Considerations in Composite Conductors: an Exposition of Percolation Theory. Advisor: David Gay. Employer: Southern Utah University. Position: Assistant Professor.
- Matthew Kruse. Smooth, Cusped, and Discontinuous Traveling Waves in the Fluid Resonance Equation. Advisor: Moysey Brio. Employer: Rincon Research Corporation, Tucson, AZ. Position: Research Mathematician.
- Olga Simek. Heat Trace Asymptotics for Domains with Singular Boundaries. Advisor: Leonid Friedlander. Employer: Lawrence Livermore National Laboratory, Computer Application Organization. Position: Computer Scientist.

## 1997

- Edward Alexander. An Investigation of the Results of a Change in Calculus Instruction at the University of Arizona. Advisor: Steve Willoughby. Employer: The University of Arizona, Tucson, AZ. Position: Adjunct Lecturer.
- Christopher Bowman. Pattern Formation and Wavelets. Advisor: Alan Newell. Employer: University of Warwick (UK). Position: Research Fellow.
- Yu-Wen Cheng. Endomorphisms of Modules over Discrete Valuation Domains. Advisor: Warren May. Employer: The Chinese Cultural University, Taipei, Taiwan. Position: Assistant Professor.
- Cheryl DeLorme. The Shafarevich-Tate Group of an Elliptic Curve. Advisor: William McCallum. Employer: The Mathematical Sciences Research Institute, Berkeley, CA. Position: Postdoctoral Fellow. Currently at Sandia National Laboratories, Albuquerque, NM..
- Cynthia Kaus. Topological and Geometrical Considerations for Maxwell's Equations on Unstructured Meshes. Advisor: Richard Ziolkowski (ECE). Employer: The University of Minnesota, Minneapolis, MN. Position: Assistant Professor.
- Amy Rabb-Liu. Teaching Methods and Student Understanding in Calculus. Advisor: Steve Willoughby. Employer: Montclair State University, New Jersey. Position: Assistant Professor.
- Stephen Shipman. A Continuum Limit of a Finite Discrete Nonlinear Schrödinger System. Advisor: Nicholas Ercolani. Employer: Louisiana State University. Position: Assistant Professor, Mathematics Department.
- Mark Torgerson. Algebraic Non-integrability of the Cohen Map. Advisor: Marek Rychlik. Employer: The National Security Agency, Ft. George G. Meade, Maryland.

## 1996

- Son-Xuan Dang. The
*C*-function for Affine Kac-Moody Algebras. Advisor: Doug Pickrell. - Javier Diaz-Vargas. On Zeros of Characteristic
*p*Zeta Functions. Advisor: Dinesh Thakur. Employer: Universidad Autónoma Metropolitana, México. Position: Profesor Titular. - Mohamed El Hadrami. Poisson Algebras and Convexity. Advisor: Hermann Flaschka. Employer: Ajman University, United Arab Emirates.
- Utith Inprasit. Equilibria In Size-Structured Population Models. Advisor: Jim Cushing. Employer: College Science, Ubon Ratchathani University, Ubon, Thailand. Position: Mathematics Professor.
- John Keisling. Approach to Equilibrium for Markovian Infinite Particle Systems with Exclusion Interaction. Advisor: William Faris. Employer: Science Applications International, Caracas, Venezuela. Position: Risk Assessment.

## 1995

- Will-Matthis Dunn II. Algorithms and Applications of Comprehensive Groebner Bases. Advisor: Marek Rychlik. Employer: Montgomery College, Conroe, TX. Position: Instructor.
- Gregory Holmberg. The Lower Bound of the Spectrum of the Dirichlet Laplacian in Unbounded Domains. Advisor: Leonid Friedlander. Employer: Al Akhawayn University Ifrane, Department of Science & Engineering, Ifrane, Morocco. Position: Assistant Professor.
- Barbara Shipman. Convex Polytopes and Duality in the Geometry of the Full Kostant-Toda Lattice. Advisor: Nicholas Ercolani. Employer: University of Texas, Arlington. Position: Assistant Professor, Mathematics Department.
- Hsin-Min Sun. Planar Nearrings and Block Designs. Advisor: James Clay. Employer: Chia Nan Junior College of Pharmacy. Position: Associate Professor.

## 1994

- Ronald Bollschweiler. Valued Modules Over Valuation Domains. Advisor: Warren May.
- Michael Brilleslyper. The Dirichlet Problem For Harmonic Maps From The Disk Into A Sphere. Advisor: Doug Pickrell. Employer: Arizona State University, Tempe, AZ. Position: Lecturer.
- Haijun Li. Contributions To The Theory of Stochastic Convexity and Stochastic Majorization. Advisor: Moshe Shaked. Employer: Washington State University, Pullman, WA. Position: Assistant Professor.
- Steven Olson. Homomorphisms of Planar Nearrings. Advisor: James Clay. Employer: University of Arizona, Tucson, AZ. Position: Adjunct Lecturer.
- Rigoberto Vera-Mendoza. Applications of Non-Standard Analysis to Locally Convex Spaces. Advisor: Carl DeVito. Employer: Universidad Michoacana, Morella, Michoacan, Mexico. Position: Professor.
- Tailiang Xie. Positive Definite Matrix-Valued Functions and Variogram Modeling. Advisor: Donald Myers. Employer: University of Arizona, Medical Center, Tucson, AZ. Position: Research Specialist.
- Chun-Woo Yang. Parameter Conditions for the Existence of Homoclinic Orbits in the Lorenz Equations. Advisor: Marek Rychlik. Employer: Hansin University, South Korea. Position: Assistant Professor.

## 1993

- Steven T. Files. Mixed Modules and Endomorphisms over Incomplete Discrete Valuation Rings. Advisor: Warren May. Employer: University of Connecticut, Storrs, CT. Position: Instructor.
- Huyi Hu. Subadditivity of Entropies of Commuting Diffeomorphisms and Examples of Non-Existence of SBR Measure. Advisor: Lai-Sang Young. Employer: University of Maryland, College Park, MD. Position: Post Doctoral Fellow.
- Matthew Klassen. Algebraic Points of Low Degree on Curves of Low Rank. Advisor: William McCallum. Employer: University of The Pacific, Stockton, CA. Position: Visiting Lecturer.
- Zheng Liu. Dynamical System and its Random Perturbations. Advisor: Lai-Sang Young. Employer: Yunnan University, ROC. Position: Faculty.

## 1992

- Christian Ballot. Density of Prime Divisors in Linear Recurring Sequences. Advisor: John Brillhart. Employer: Université de Caen, Caen, France. Position: Faculty.
- Jian Cheng. Horseshoes in the Standard Map. Advisor: Maciej Wojtkowski. Employer: Nanjing University, Nanjing, PRC. Position: Junior Faculty.
- Wen-Fong Ke. Structures of Circular Planar Nearrings. Advisor: James Clay. Employer: National Cheng Kung University, Tainan, ROC. Position: Associate Professor.
- Chi-Kun Lin. On The Incompressible Limit of The Compressible Navier-Stokes Equations. Advisor: David Levermore. Employer: National Cheng Kung University, Tainan, ROC. Position: Associate Professor.
- Janet McShane. Computation of Polynomial Invariants of Finite Groups. Advisor: Larry Grove. Employer: Northern Arizona University, Flagstaff, AZ. Position: Associate Professor.
- Tai-Cheng Tso. The Zero Dispersion Limits of Nonlinear Wave Equations. Advisor: David Levermore. Employer: Kaohsiung Normal University, Kaohsiung, Taiwan, ROC. Position: Associate Professor.
- Haolong Zhu. Some Contributions to Reliability Theory. Advisor: Moshe Shaked. Employer: Pima Community College, Tucson, AZ. Position: Instructor.
- Maorong Zou. Geometry of Two Degree of Freedom Integrable Hamiltonian Systems. Advisor: Hermann Flaschka. Employer: University of Texas, Austin, TX. Position: Instructor.