Mathematics : Research Interests

Professors

1. William K Allard, Scientific computing, particularly distributed computing; differential geometry; geometric measure theory; partial differential equations.
2. Paul S Aspinwall, String Theory
3. J. Thomas Beale, Partial Differential Equations and Fluid Mechanics
4. Hubert L. Bray, Geometric Analysis, General Relativity
5. Robert L Bryant, Nonlinear Partial Differential Equations and Differential Geometry
6. Richard M Hain, Topology of Algebraic Varieties, Hodge Theory, and Moduli of Curves
7. John Harer, Computational Topology, Computational Geometry, Computational Biology, Algorithms
8. Harold Layton, Mathematical Physiology
9. William L Pardon, Algebra and Geometry of Varieties
10. Arlie O Petters,
    Mathematical Physics - Gravitational Lensing, General Relativity, Astrophysics, Cosmology
    Mathematics - Differential Geometry, Singularity Theory, Probability Theory

    My current research deals with employing weak and strong deflection gravitational lensing to test theories of gravity, explore the geometry of spacetime around black holes, and probe the nature of dark matter on galactic scales. I utilize tools from astrophysics, cosmology, general relativity, high energy physics, and a variety of mathematical fields (e.g., differential geometry, singularity theory, and probability theory).

    A mathematical theory of gravitational lensing is presented in the following book:
    Singularity Theory and Gravitational Lensing.

11. Michael C Reed, Analysis, Applications of Mathematics to Physiology and Medicine
12. Leslie D. Saper, Locally symmetric varieties, Automorphic forms,
    L²-cohomology and intersection cohomology, Geometrical analysis of singularities
13. David G Schaeffer, Applied Mathematics, especially Partial Differential Equations
14. Chad Schoen, Algebraic Geometry
15. Mark A Stern, Geometric Analysis,string theory
16. John Trangenstein, Adaptive mesh refinement, Multigrid preconditioners
17. Stephanos Venakides, Integrable systems, Wave motion in complex media, Mathematical biology
18. Xin Zhou, Partial Differential Equations and Integrable Systems

Associate Professors

1. David Kraines, Algebraic Topology and Game Theory
2. Jonathan C. Mattingly, Applied mathematics, Probability, Ergodic Theory, Stochastic partial differential equations, Stochastic dynamical systems, Stochastic Numerical methods, Fluids
3. M. Ronen Plesser, String Theory and Quantum Field Theory
4. Thomas P Witelski, Fluid Dynamics, Perturbation Methods, Asymptotic Analysis, Nonlinear Ordinary and Partial differential equations

Assistant Professors

1. Mark Huber, Monte Carlo simulation and stochastic computation
2. Anita Layton, Mathematical physiology; Multiscale numerical methods; Numerical methods for global atmospheric models
3. Mauro Maggioni, Harmonic analysis, with applications to statistical analysis of high-dimensional data, machine learning, imaging.
4. Lenhard Ng, Symplectic geometry, Low dimensional topology, Contact geometry, Knot theory, Holomorphic curves

Assistant Research Professors

1. Matthias Heymann, computation of transition paths for rare events, application to biology
2. Dan A. Lee, Geometric Analysis, Geometric Topology
3. Shahed Sharif, Arithmetic geometry, number theory

Professors of the Practice of Mathematics

1. Lewis D Blake, Teaching mathematics
2. Jack Bookman, Mathematics Education
3. Clark B Bray, Algebraic Topology

Adjunct Professors

1. Andrea L Bertozzi, Nonlinear Partial Differential Equations, Applied Mathematics, Thin films, Image Processing, Swarming
2. Jonathan Hanke, Number Theory, Automorphic forms, and Quadratic forms
3. Michael Shearer, Partial Differential Equations; Granular Materials; Thin Liquid Films.
4. Jonathan Wahl, Algebraic Geometry

Professors Emeriti

1. Richard E Hodel, Set-theoretic Topology, set theory, logic
2. Joseph Kitchen, Functional Analysis
3. Lawrence C Moore, Mathematics Education and Functional Analysis

4. David A Smith, Mathematics Education

Instructors

1. Timothy Lucas, Numerical Analysis, Partial Differential Equations, Multigrid, Stochastic Differential Equations and Parallel Computing

Post Docs/Research Associates

1. Anne Catlla, Mathematical modeling in biology and pattern formation

Visiting Faculty

1. Benoit Charbonneau, Gauge theory, more specifically Nahm transforms, Yang-Mills instantons, and their dimensional reductions
2. Boumediene Hamzi, Applied Dynamical Systems, Control Theory
3. Fernando A. Schwartz, Differential Geometry

Graduate Students

1. Amir Babak Aazami, Gravitational Lensing, Singularity Theory
2. Prakash Balachandran, Stochastic Differential Geometry and Infinite Dimensional Random Walks
3. 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
4. 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.
5. Matthew Bowen, PDEs, Numerical Analysis
6. David Cesa, Numerical Analysis
7. Benjamin Cooke, Genetics
8. Mihaela K. Froehlich, Rotating thin films
9. Oliver Gjoneski, Algebraic Geometry, Algebraic Groups, Langlands Program
10. Daniel Goldstein, I am working on a numerical approach to solving Riemann-Hilbert problems.
11. Michael B. Gratton, Dewetting and coarsening of thin fluid films
12. Aubrey R. HB, Computational Algebraic Topology
13. Aaron Jackson, Analysis, PDEs
14. Jeff Jauregui, General Relativity, geometric flows
15. 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.
16. 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.
17. Wai J. Law, Applied Math
18. 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. My current interest is in probabilistic models of ecological systems.
19. Janice M. McCarthy, Mathematical Physics
20. Anthony J. Narkawicz, Algebraic Topology, Hyperplane Arrangements, Local System Cohomology
21. 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.
22. Michael Pruitt, Analysis, Focus Undecided
23. David Rose, I am currently interested in topology and geometry, especially with an algebraic flavor. My research as an undergraduate was in the area of matrix analysis. More specifically, I studied properties of the Aluthge transform and the numerical range.
24. Arya Roy, String theory
25. Lauren M. Shareshian, I am studying integrable systems under Stephanos Venakides.
26. Abraham D. Smith, Differential Geometry, Geometric PDE, Exterior Differential Systems
27. Joseph A. Spivey, Algebraic Topology
28. Matthew W. Surles, Scientific Computing, Analysis, Potential Theory
29. Tiffany N. Tasky, Stochastic Analysis
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