Mathematics Colloquia and Seminars
Return to Colloquia & Seminar listing
|Speaker: ||Victor Ostrik, MIT|
|Location: ||693 Kerr|
|Start time: ||Wed, Jan 22 2003, 4:10PM|
I will talk about my joint work with P.Etingof and D.Nikshych.
A categorification is a procedure in which one replaces integer numbers
by vector spaces, vector spaces by categories, maps between
vector spaces by functors etc. Surprisingly enough such an
abstract procedure is related to physics (here is a typical
slogan: a categorification of $d-$dimensional topological
field theory is $(d+1)-$dimensional topological field theory).
In this talk I will explain the simplest way to categorify
ring theory. In this theory rings are replaced by fusion
categories (= semisimple rigid monoidal categories with finitely
many simple objects) and modules over rings are replaced by
module categories. Our main result is the following Theorem:
fusion categories and module categories over them admit no
deformations. Thus it is reasonable to try to classify these
objects. The problem of classification of fusion categories
and module categories over them appears to be closely related
to Operator Algebras and to Conformal Field Theory. I will review
some results in this direction.
3:45 Refreshments will be served before the talk in 551 Kerr Hall