Chairman's Introduction, Robert Fefferman | Faculty Research Summaries

The research activities of the Department of Mathematics cover a wide variety of areas reflecting the expanse of modern mathematics. As mathematics has diversified, the interconnections between various directions have deepened and become much richer, so that one sees a remarkable fundamental unity and cohesion of mathematics within a situation in which there are constantly new directions evolving. The Mathematics Department is committed to this perspective both in terms of research and educating graduate students.

Mathematics has always reflected our perceptions of external phenomena and often contributed to our understanding of it. The Department has members with joint appointments in Physics, Statistics and Computer Science, and there is very significant and productive interdisciplinary activity in the relationship both to these areas and to mathematical biology and astrophysics as well.

While there is more detail discussed by individual faculty members below, some of the broad areas in which there is very significant research activity in the department include: algebraic geometry and commutative algebra, number theory, representation theory, finite groups, logic, Lie groups, algebraic topology, manifolds, differential geometry, ergodic theory, complex geometry, harmonic analysis, partial differential equations, numerical analysis, fluid flow, computational mathematics, and neural networks.

In addition to the regular members of the department, there are a large number of junior faculty, a very active visitor's program, and an excellent and diverse graduate student body.

Faculty Research Summaries