Mathematics Grad: Research Interests

Graduate Students

  1. Amir Babak Aazami, Gravitational Lensing, Geometry, Singularity Theory
  2. Alex Aguado, Geometric & Differential Topology, Foundations, Graph Theory
  3. Prakash Balachandran, Stochastic Differential Geometry and Infinite Dimensional Random Walks
  4. Matthew M. Bowen, PDEs, Numerical Analysis
  5. Benjamin Cooke, Genetics
  6. Mihaela K. Froehlich, Rotating thin films
  7. Oliver Gjoneski, Algebraic Geometry, Algebraic Groups, Langlands Program
  8. Michael B. Gratton, Dewetting and coarsening of thin fluid films
  9. Aubrey R. HB, Computational Algebraic Topology
  10. Aaron Jackson, Analysis, PDEs
  11. Jeff Jauregui, General Relativity, geometric flows
  12. 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.
  13. Hyeongkwan Kim, algebra, topology, geometry
  14. Tiffany N. Kolba, Stochastic Analysis
  15. 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.
  16. Wai J. Law, Applied Math
  17. Shishi Luo, Though I originally did my undergraduate degree with the aim to do mathematical modeling in finance, I've since discovered that mathematics also has a multitude of applications in biology. I recently did a project modeling the spread of avian flu on a scale-free network.
  18. Janice M. McCarthy, Mathematical Physics
  19. Anthony J. Narkawicz, Algebraic Topology, Hyperplane Arrangements, Local System Cohomology
  20. Alan Parry, Currently I'm interested in Differential Geometry and its applications to Relativity Theory. In the past, I have studied Lie Theory and my master's thesis was on classifying solvable Lie algebras through dimension seven.
  21. Harrison Potter, Learning.
  22. Michael Pruitt, Analysis, Focus Undecided
  23. David Rose, I am currently interested in homological algebra, algebraic topology, algebraic geometry, and category theory. My research as an undergraduate was in the areas of matrix analysis and operator theory. More specifically, I studied properties of the Aluthge transform and the numerical range.
  24. Arya Roy, String theory
  25. Abraham D. Smith, Differential Geometry, Geometric PDE, Exterior Differential Systems, Mathematics Education
  26. Joseph A. Spivey, Algebraic Topology
  27. Rachel Thomas, I'm interested in stochastic differential equations on graphs and the mathematics of biochemical reaction networks.
  28. Andrea Watkins, Stochastic Partial Differential Equations
  29. Jason Wilson, I am interested in solving Stoke's flow problems in 3D using boundary integral methods.
  30. Feng Xu, Nonlinear Partial Differential Equations and Differential Geometry