New Paradigms in Invariant Theory

Abstract

Since its beginnings in the early 19th century, invariant theory has provided impetus for advances in algebra, especially commutative algebra. This continues today, especially with the use of toric deformation to understand the structure of rings arising in invariant theory and representation theory. This talk will review the general notion of toric deformation and some of its applications in invariant theory. Special attention will be given to the class of Hibi rings. These rings have a particularly elegant theory, with strong connections to combinatorics, and they encompass many of the rings that appear in key applications of toric deformation.

About the speaker

Prof. Howe received his PhD from UC Berkeley in 1969, and has been a faculty member of Yale University since 1974. He was appointed William R. Kenan Jr. Professor of Mathematics in 2002. His mathematical research investigates symmetry and its applications. He is well-known for his contributions to representation theory, and in particular for the notion of a reductive dual pair, sometimes known as a Howe pair. He is a Fellow of the American Academy of Arts and Sciences and a Member of the US National Academy of Sciences.