Schedule of talks:

Abstracts

(Oh): In this talk, we will review the basic constructions of Lagrangian Floer theory and explain its obstruction-deformation theory and how the A_\infty structure and Fukaya category naturally arises. If time permits, we will also indicate what roles these structure would play in the point of pure symplectic topology too.

(Cho): In the last decade, the Lagrangian Floer theory for toric manifolds has been extensively studied and has shown interesting Hamiltonian dynamics and mirror symmetry phenomenon, and we plan to review the basic ideas of these developments. We will discuss about an extension of such theory for toric orbifolds if time permits.

(Wang): For a topological space and a loop of homeomorphisms, one can construct a fiber bundle over sphere by the clutching construction, namely one takes two copy of disks, products them with the topological space and then glues them along the boundary according to the loop of homeomorphisms. If we start with a symplectic manifold $(M,\omega)$ and a loop of Hamiltonian diffeomorphisms, the fiber bundle we get will possess a symplectic structure over the total space. Using this construction, P. Seidel defined a homomorphism from the fundamental group of its Hamiltonian diffeomorphisms $\pi_{1}(Ham(M,\omega))$ to the multiplication group of the quantum cohomology ring $QH^{*}(M,\omega)$. This homomorphism is now called Seidel representation. With Seidel representation, one can study $QH^*(M,\omega)$ with $\pi_1(Ham(M,\omega))$, and vice versa. In this talk, I will explain the construction of Seidel representation and introduce some applications via examples. If time allows, I will also say a little about its generalization to symplectic orbifolds which is a joint work with Hsian-Hua Tseng.

This page is maintained by  Hsian-Hua Tseng
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