## EVENT DETAILS AND ABSTRACT

**Geometry/Physics Seminar**
**Title:** Counting finite dimensional irreducible representations over quantizations of symplectic resolutions.

**Speaker:** Ivan Loseu

**Speaker Info:** Northeastern University

**Brief Description:**

**Special Note**:

**Abstract:**

A basic problem in Representation theory is, given an algebraic object such as
a group, an associative algebra or a Lie algebra, to study its finite dimensional irreducible
representations. The first question, perhaps, is how many there are. In my talk I will address
this question for associative algebras that are quantizations of algebraic varieties admitting
symplectic resolutions. Algebras arising this way include universal enveloping algebras
of semisimple Lie algebras, as well as W-algebras and symplectic reflection algebras. The
counting problem is a part of a more general program due to Bezrukavnikov and Okounkov
relating the representation theory of quantizations to Quantum cohomology of the underlying
symplectic varieties. It is also supposed to have other connections to Geometry. I will consider
the case of quotient singularities and will make the exposition non-technical.

**Date:** Thursday, January 9, 2014

**Time:** 4:00pm

**Where:** Lunt 107

**Contact Person:** Michael Couch

**Contact email:** mcouch@math.northwestern.edu

**Contact Phone:**

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