Symmetry of Symmetries: Ramifications of Invariant Theory in Mathematics and Physics

Abstract

In his famous text, the Classical Groups, Prof Hermann Weyl presented the First and Second Fundamental Theorem of Invariants for the standard actions of the classical groups. As formulated by Prof Weyl, these results were elegant but seemingly self-contained.

However, developments of the latter decades of the 20th century revealed deep connections of this topic with fundamental results and phenomena across a wide range of fields, from physics to number theory to analysis to homological algebra and algebraic geometry.

Moreover, although invariant theory is primarily concerned with symmetry under group actions, these connections involve another level of symmetry that connects different actions of different groups. This talk will review the several stages of these developments, which may now be nearing completion.

About the speaker

Prof. Roger Howe received his PhD from the University of California at 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. He is also Visiting Professor of the HKUST Jockey Club Institute for Advanced Study. 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.