Chelsea Walton, Massachusetts Institute of Technology
“Noncommutative Invariant Theory”
Invariant Theory is a beautiful field. The area dates back over 100 years to the work of Hilbert, Klein, Gauss, and many others. It is a very active area of research today, particularly from the view- point of algebraic geometry and combinatorics. It also has far reaching applications in representation theory, coding theory, mathematical modeling, and even air target recognition. (I just happened to run across this last application on google; it will *not* be explained.)
In this talk, I hope to illustrate the beauty of a new and fast-paced field: Noncommutative Invariant Theory. All basic notions will defined. I will explain the noncommutative analogues of each of the following terms: ”groups”, ”acting on”, and ”polynomial rings”. If time permits, I will also provide an overview of recent work pertaining to Hopf algebra actions on (noncommutative) regular algebras. The results discussed here are from joint works with Kenneth Chan, Pavel Etingof, Ellen Kirkman, Yanhua Wang, and James Zhang: see arXiv:math/1210.6432, 1211.6513, 1301.4161, 1303.7203.
Refreshments will be served in MC 5046 at 3:30 p.m. Everyone is welcome to attend.