Mathematics Grad: Research Interests

Graduate Students

1. Amir Babak Aazami, Gravitational Lensing, Singularity Theory
2. Alex Aguado, Geometric & Differential Topology, Foundations, Graph Theory
3. Prakash Balachandran, Stochastic Differential Geometry and Infinite Dimensional Random Walks
4. Sergey Belov, My research interests include the Riemann-Hilbert approach to integrable systems (KdV, NLS, sine-Gordon) and analysis of turning points/Stokes lines in WKB method. In particular, my current project is studying analytically as well as numerically the second break of the asymptotic solution of the semiclassical focusing nonlinear Schrodinger equation (NLS). This is closely related to scattering/inverse scattering for linear operators (Schrodinger, Zakharov-Shabat) where time is a parameter.
   
   Research Statement
5. Paul L. Bendich, I work in computational topology, which for me means adapting and using tools from algebraic topology in order to study noisy and high-dimensional datasets arising from a variety of scientific applications. My thesis research involves the analysis of datasets for which the number of degrees of freedom varies across the parameter space. The main tools are local homology and intersection homology, suitably redefined in this fuzzy multi-scale context. I am also working on building connections between computational topology and various statistical data analysis algorithms, such as clustering or manifold learning.
6. Matthew Bowen, PDEs, Numerical Analysis
7. David Cesa, Numerical Analysis
8. Benjamin Cooke, Genetics
9. Mihaela K. Froehlich, Rotating thin films
10. Oliver Gjoneski, Algebraic Geometry, Algebraic Groups, Langlands Program
11. Daniel Goldstein, I am working on a numerical approach to solving Riemann-Hilbert problems.
12. Michael B. Gratton, Dewetting and coarsening of thin fluid films
13. Aubrey R. HB, Computational Algebraic Topology
14. Aaron Jackson, Analysis, PDEs
15. Jeff Jauregui, General Relativity, geometric flows
16. 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.
17. Tiffany N. Kolba, Stochastic Analysis
18. 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.
19. Wai J. Law, Applied Math
20. 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.
21. Janice M. McCarthy, Mathematical Physics
22. Anthony J. Narkawicz, Algebraic Topology, Hyperplane Arrangements, Local System Cohomology
23. 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.
24. Michael Pruitt, Analysis, Focus Undecided
25. 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.
26. Arya Roy, String theory
27. Abraham D. Smith, Differential Geometry, Geometric PDE, Exterior Differential Systems, Mathematics Education
28. Joseph A. Spivey, Algebraic Topology
29. Matthew W. Surles, Scientific Computing, Analysis, Potential Theory
30. Rachel Thomas, I'm interested in stochastic differential equations on graphs and the mathematics of biochemical reaction networks.
31. Andrea Watkins, Stochastic Partial Differential Equations
32. Jason Wilson, I am interested in solving Stoke's flow problems in 3D using boundary integral methods.
33. Feng Xu, Nonlinear Partial Differential Equations and Differential Geometry