This award provides support for International Press Lecture Series II: Invariant Theory and Combinatorics of Representations, which will be held at the University of California at Irvine in January 1997. The conference will emphasize the interdisciplinary nature of representation theory. Roger Howe will give the three main one-hour lectures. Other participants in the conference will come from the disciplines of geometric invariant theory, combinatorics, representation theory, and group theory. There will be ten supplementary lectures from mathematicians in these disciplines. The subject matter of this conference is connected to several different areas of mathematics, including invariant theory and combinatorics. In general, invariant theory involves the actions of linear algebraic groups on manifolds or linear spaces and the determination of the mathematical invariants of the space under these group actions. Combinatorics attempts to find efficient methods to study how discrete collections of objects can be arranged. The behavior of discrete systems is extremely important to modern communications.
