Central Ohio Symplectic Geometry Day 

  November 7, 2011, Ohio State University

Location: CH 240
Organizer: Hsian-Hua Tseng
Sponsor: Mathematics Research Institute

Schedule of talks:


November 7, 2011 
Mon, 10:30--11:30am
CH 240 
Yong-Geun Oh  
(University of Wisconsin-Madison) 
Lagrangian Floer homology and its deformations
November 7, 2011 
Mon, 11:45am--12:45pm
CH 240 
Cheol-hyun Cho 
(Seoul National University) 
Lagrangian Floer cohomology for toric manifolds and orbifolds
November 7, 2011 
Mon, 2:30--3:30pm
CH 240 
Dongning Wang 
(University of Wisconsin-Madison) 
Seidel representation and its applications


(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.

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