Leonardo da Vinci Building Luigi Stasi Seminar Room
Strada Costiera, 11
I - 34151 Trieste (Italy)
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.
ICTP - Strada Costiera, 11
I - 34151 Trieste Italy (+39) 040 2240 111 email@example.com