Exceptional Structures and Symmetry

Abstract

The idea of symmetry gives people insight into both art and the fundamental structures on which the world is built. The effort to understand the mathematical aspects of symmetry has led to discovery of a variety of exceptional and beautiful mathematical structures, from the discovery in classical times of the Platonic solids, to Lie groups, root systems, the Leech lattice and the sporadic finite groups, of which the largest is the Monster. This talk will survey some of these exceptional structures and discuss relationships between them, with a focus on the 24-cell, a totally unique 4-dimensional regular solid.

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. 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.