Harrelson News–2000
Faculty Research
Most of the faculty loosely group into six research areas:
ALGEBRA
Lie theory
Professors Fauntleroy, Helminck, Jing, Misra, Putcha, and Stitzinger. Structure and representations of Lie groups, Lie algebras, and monoids of Lie type, including quantum groups, vertex operator algebras, and applications to combinatorics.
Associative algebra
Professors Chung, Cohen, Hartwig, Koh, and Luh. Ring theory, topological algebra, and matrix theory.
Symbolic computation
Professors Hong, Kaltofen, Latch, and Singer. Design and implementation of symbolic software, such as software for factori-zation, solution of equations, and symbolic integration of differential equations; verification of algorithms.
DIFFERENTIAL EQUATIONS AND CONTROL
Dynamical systems
Professors Franke, Lin, Marlin, Rodriguez, Schecter, and Selgrade. Applications of dynamical systems and bifurcation theory to biological systems, singular perturbation phenomena, and shock waves; nonlinear operator equations.
Partial differential equations
Professors Fouque, Martin, Pao, Reitich, and Shearer. Analytic and numerical study of nonlinear partial differential equations of elliptic, parabolic, and hyperbolic types, including applications to mechanics and reaction-diffusion systems.
Control
Professors Banks, Chukwu, Fitzpatrick, Ito, McEneaney, Smith, and Tran. Control, parameter estimation, inverse problems, computational methods, and modeling issues for PDE, delay, and stochastic models, including problems involving flexible structures, smart materials, acoustics, fluids, physiology, economics, and finance.
NUMERICAL ANALYSIS AND OPTIMIZATION
Professors Campbell, Chu, Dunn, Gremaud, Ipsen, Kelley, Li, Meyer, Scroggs, Siewert, and White. Development and analysis of computational methods for systems of linear and nonlinear equations, ordinary and partial differential equations, differential algebraic equations, and optimization and optimal control problems.
PROBABILITY
Professors Bishir, Fouque, Hitczenko, and Silverstein. Probability theory, including martingale inequalities; random matrices; and applications to population biology.
MATHEMATICAL PHYSICS
Professors Brown, Fulp, Kheyfets, and Norris. Applications of differential geometry to geometric mechanics, quantum mechanics, general relativity, field theory, quantum gravity, and relativistic astrophysics.
TOPOLOGY
Professors Chandler, Faulkner, and Lada. General topology, especially Hausdorff compactifications, and applications of algebraic topology to mathematical physics.