Mathematics Grad: Research Interests

Graduate Students

1. Amir Aazami, Gravitational Lensing, Singularities, General Relativity, Geometry
2. Alex Aguado, Geometric & Differential Topology, Foundations, Graph Theory
3. Prakash Balachandran, Harmonic Analysis, Probability, Stochastic Processes
4. Matthew M. Bowen, PDEs, Numerical Analysis
5. Benjamin Gaines, Algebra
6. Oliver Gjoneski, Algebraic Geometry, Algebraic Groups, Langlands Program
7. Aubrey R. HB, Computational Algebraic Topology
8. Aaron D. Jackson, Analysis, PDEs
9. Jeff Jauregui, general relativity, geometric analysis, geometric flows
10. Michael J. Jenista, I am currently working on the application of the Conley Index to biological dynamics. The Conley Index is a generalization of Morse Theory, and lends itself to computer work. I am employing software developed by Konstantin Mischaikow, Pawel Pilarczyk, Marian Mrozek, and others to study dynamical changes in coupled oscillator networks over various parameter ranges.
11. Hyeongkwan Kim, algebra
12. Tiffany N. Kolba, Stochastic Analysis
13. M. George Lam, I study curvature in general relativity under Dr Hubert Bray. Recently I have been investigating the question of defining mass in a spacetime. The mass of an entire spacetime have been studied extensively over the past few decades with many fundamentals results, two of which are the Positive Mass Theorem and the Penrose Inequality. On the other hand, the question "How much matter is in a given region of a spacetime?" is still very much an open problem. Various definitions of this so called quasi-local mass have been proposed, but none satisfies all the desirable properties one would expect in such a definition.
    
    Besides being interesting in their own rights, such quasi-local mass functions have turned out to be important tools in understanding the geometry of spacetime. Husiken and Illamen proved the Riemannian Penrose Inequality for a single black hole via inverse mean curvature flow and the Hakwing mass, and Bray used the conformal mass to prove case with any number of black holes. More recently, Shi and Tam obtained lower bounds for the Brown-York mass and the Bartnik mass for compact three manifolds with smooth boundaries and derived sufficient conditions for the existence of horizons for a certain class of compact manifolds as a consequence. All these lead to the idea that a 'good' definition of quasi-local mass should also provide us with insights into the general structure of spacetime.
14. Junchi Li, Probability Theory and Its Applications
15. Shishi Luo, Modeling the ecology and evolution of infectious diseases
16. Christopher O'Neill, Combinatorics
17. Alan R. Parry, Differential Geometry, General Relativity, Lie Theory
18. Harrison D. Potter, Real, Complex, and Functional Analysis
19. Michael D. Pruitt, Analysis
20. David E. Rose, I am currently interested in Khovanov homology and categorification. More generally, I am interested in knot theory, algebraic topology, homological algebra, category theory, and algebraic geometry. As an undergraduate I worked in the areas of matrix analysis and operator theory. Specifically, I studied properties of the Aluthge transform and the numerical range.
21. Arya Roy, String theory
22. Rachel L. Thomas, I'm interested in stochastic differential equations, mathematical modeling, stochastic processes, and biochemical reaction networks.
23. Tatsunari Watanabe, Commutative Algebra, Algebraic Geometry, Topology
24. Andrea C. Watkins, Stochastic Partial Differential Equations
25. Jason R. Wilson, I am interested in solving Stoke's flow problems in 3D using boundary integral methods.
26. Hangjun Xu, Geometry