## EVENT DETAILS AND ABSTRACT

**Geometry/Physics Seminar**
**Title:** Equivariant Lagrangian branes and Representations

**Speaker:** Yanki Lekili

**Speaker Info:** UIC

**Brief Description:**

**Special Note**:

**Abstract:**

Classical Bott-Borel-Weil theory constructs irreducible
representations of semisimple Lie algebras on the section spaces of
homogeneous vector bundles on homogeneous spaces. In this talk, we
decribe a construction in symplectic geometry which is meant to serve as
the mirror dual to Bott-Borel-Weil construction. Building on
Seidel-Solomonâ€™s fundamental work, we define the notion of an
"equivariant Lagrangian brane" in an exact symplectic manifold (which is
meant to be the mirror dual of a homogenous variety G/P), and construct
representations of the Lie algebra g=Lie G, on Floer cohomology of
equivariant Lagrangian branes. We will make our construction completely
explicit in the case of sl_2 and comment on generalizations to arbitrary
semisimple Lie algebras. This is a joint work with James Pascaleff.

**Date:** Thursday, October 2, 2014

**Time:** 4:00pm

**Where:** Lunt 107

**Contact Person:** Mihnea Popa

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

**Contact Phone:**

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