Simons Center Program in Homological Mirror Symmetry, Symplectic
Topology, and Invariants of Low Dimensional Manifolds
Spring 2011
Program Description. The subprogram in Homological Mirror Symmetry and
Symplectic Topology is organized by Paul Seidel. The subprogram on Invariants
of Low Dimensional Manifolds is organized by Mikhail Khovanov and Peter
Ozsvath. In addition to Khovanov and Seidel, who are spending the entire
semester at the Center, Dmitri Orlov, Chris Woodward, and Jake Rasmussen are
members of this program in residence for the entire semester. The topics for the
program include lagranian submanifolds, Floer homology and the resulting
Fukaya Category associated to a symplectic manifold as well as explicit
descriptions of the Fukaya category in terms of generators and relations for
explicit examples. A closely related topic is Homological Mirror Symmetry,
especially for low dimensional manifolds (complex dimension 1,2,3). The
subprogram on Invariants of low Dimensional Manifolds includes categorification
of various mathematical structures, knot invariants, and three-manifold
invariants, as well as gauge theoretic invariants — Heegaard Floer homology and
a gauge-theoretic approach to Khovanov homology as recently introduced by
Witten.
There are two workshops associated with these programs: one
entitled “Equivariant Quantum Cohomology, Mirror Symmetry, and Symplectic
Geometry” from May 16 – 20, 2011 and one entitled “Homological Invariants in
Low-Dimensional Topology Workshop” from June 13 – 17, 2011.
Homological Mirror Symmetry, Symplectic Topology:
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Invariants of Low Dimensional Manifolds
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