Mathematics Seminar next week

[math]

MATHEMATICS SEMINARS - 2011


Tuesday, 19 July, at 14:30 hrs

Dr. Sikimeti Ma'u
(MSRI, Berkeley, USA)


"Lagrangian correspondences in symplectic topology"

Abstract

I'll give an overview of Lagrangian Intersection Floer homology,
and its extension to Fukaya's A-infinity categories.  These
are the basis for the symplectic side of Kontsevich's Homological Mirror 
Symmetry conjecture relating the algebraic geometry and symplectic 
geometry of mirror pairs of Calabi-Yau manifolds.  The constructions are 
defined by counts of pseudoholomorphic curves in a symplectic manifold, 
with Lagrangian submanifolds as boundary conditions.  The recent 
pseudoholomorphic quilt theory of Wehrheim and Woodward incorporates 
Lagrangian correspondences as additional
boundary conditions, so that pseudoholomorphic quilts transition between 
pseudoholomorphic curves in one symplectic manifold to pseudoholomorphic 
curves in another.  I will explain how this leads to constructions of 
A-infinity bimodules associated to Lagrangian correspondences, and an 
enhancement to A-infinity functors.
These may be viewed as symplectic analogues of Fourier-Mukai transforms 
in algebraic geometry.  Joint work with Wehrheim and Woodward.

Venue: Luigi Stasi Seminar Room, ICTP Leonardo Building, first floor.