Schedule of talks:

Abstracts

(Tseng): In this talk we will present an identity that equates certain expression of orbifold Hodge numbers and certain expression of orbifold Chern numbers. This generalizes a theorem of Libgober and Woods.

(Tu): We compute the Hochschild cohomology of An A-infinity algebra whose derived category is the derived category of Matrix Factorizations. It turns out that it is the Jacobi ring of the potential function.

(Parker):

(Albers): Leonid Polterovich exhibited a beautiful Lagrangian torus in T*S^2 and asked if this torus is Hamiltonianly displaceable. In joint work with Urs Frauenfelder we prove that the Lagrangian Floer homology does not vanish, indeed equals the singular homology of the torus. In particular, this gives a negative answer to Polterovich's question. In the talk I will describe the construction of the Lagrangian torus and present the computation of the Lagrangian Floer homology which is based on an symmetry argument.
This talk does not assume detailed familiarity with Floer homology.

(Poon): It is well known that given a complex structure J on a manifold M there is a differential Gerstenhaber algebra DGA(M, J). Similarly, given a symplectic structure \omega, there is a differential Gerstenhaber algebra DGA(N, \omega). They form a weak mirror pair if DGA(M, J) and DGA(N, \omega) are quasi-isomorphic. In this talk, we provide a preliminary report on a complete description of weak mirror pairs of six-dimensional nilmanifolds.

(Wade): Let M be a smooth finite-dimensional manifold. Every Poisson structure on M gives rise to a natural foliation of M whose leaves are symplectic manifolds (possibly of different dimensions). A leaf L of a Poisson structure on M is stable if every nearby Poisson structure admits a nearby leaf L', which is diffeomorphic to L.
In this talk, we discuss stability of symplectic leaves of a Poisson structure. Of particular interest is the case of zero-dimensional leaves, called singular points. We will give sufficient conditions for stability of singular points. We will provide some examples for Poisson manifolds of dimension less than 5.

(Costello): To a Calabi-Yau category one can associate a two dimensional field theory, satisfying axioms similar to those of Gromov-Witten theory. The partition function of this theory is the analog of the generating function for Gromov-Witten invariants. For example, the partition function of the derived category of coherent sheaves on a Calabi-Yau manifold is conjectured to be the same as the generating function for the Gromov-Witten invariants of the mirror. This talk will describe an algorithm for calculating the partition function associated to any Calabi-Yau category.

(Westerland): This is a report on work in progress with Nathalie Wahl. We'll define string topology operations for classifying spaces of compact Lie groups (using the work of Chataur-Menichi), study some examples, and sketch a vanishing result in twice the stable range.

(Haesemeyer): Algebraic K-theory is an invariant of rings and varieties that is almost impossible to compute, even for fields. However, it turns out that the so-called Nil K-theory, a direct factor in the K-theory that vanished for regular rings, can be calculated using Hochschild homology. I will try to explain why this is the case, and give some applications.

(Oh): In this talk, I will introduce the notion of weakly unobstructed Lagrangian submanifolds and balanced Lagrangian submanifolds. I will explain construction of certain potential function constructed out of study of deformation theory of Floer cohomology and explain its relationship to the earlier work of Givental which advocates that quantum cohomology ring is isomorphic to the Jacobian ring of Landau-Ginzburg superpotential. I will explain these result in the context of mirror symmetry between Fano toric A-model and Landau-Ginzburg B-model.

(Kieserman): Coisotropic submanifolds have a symplectic aspect, and a foliations aspect. Deformation of foliations is a rather under-determined problem, but the additional symplectic structure allows for computable results. I will talk about my thesis work on computing obstructions in the L-infinity algebra governing this deformation problem, due to Oh & Park. My talk will be very geometric.

(Solomon): I will begin with an overview of open Gromov-Witten theory for 4 and 6 dimensional targets, focusing on the problem of disk enumeration in the projective plane. The solution is given via an open analogue of the WDVV equation. Then I will describe recent work with R. Pandharipande on the open Gromov-Witten theory of the point. Using the open WDVV equation to determine the genus 0 theory of the point, we extrapolate to higher genus and find an open analogue of the KdV hierarchy.

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