Department of Mathematics 2002

The principal research interests of the department lie in the two general areas of mathematical analysis and it applications, and of algebra, mainly representation theory, algebraic geometry, and number theory. Topics covered in analysis include structure of finite and infinite dimensional spaces, operator and matrix theory, function theory on the plane, graphs and Riemann surfaces, spectral theory, several aspects of probability and some applications of statistics, linear and nonlinear ordinary and partial differential equations, harmonic analysis, dynamical systems, control theory in its various manifestations, optimization, game theory, approximation and complexity of functions, numerical analysis, singularity theory, and robotics. The algebraic direction includes some aspects of algebraic geometry, representation theory, quantum groups, number theory, automorphic forms, ring theory, and enveloping algebras. Although the approach taken is primarily that of theoretical mathematics, some of the research leans towards possible applications.