Symplectic Geometry Seminar

Wednesday 3:30pm-5:00pm VV B139

• If you would like to talk in the seminar but have difficulty with adding information here, please contact Dongning Wang

date	speaker	title	host(s)
09/19	Rui Wang	The canonical connection on contact manifolds
09/26	Rui Wang	An tensorial proof of exponential decay of pseudo-holomorphic curves on contact manifolds
10/03	Erkao Bao, Jaeho Lee	Symplectic Homology1
10/10	Dongning Wang, Jie Zhao	Symplectic HomologyII
10/17		no seminar this week
10/24	Wenfeng Jiang	Classification of Free Hamitolnian-its mathematics foundation
11/07	Dongning Wang	Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation
11/28	Yoosik Kim	Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group
12/05	Yoosik Kim	Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group(continued)
12/12	Yunfeng Jiang	an introduction on the geometry of spin equations

Abstracts

Rui Wang The canonical connection on contact manifolds and an tensorial proof of exponential decay

Abstract:

We define a new connection on contact manifolds and give the proof of its existence and uniqueness. This is an odd dimensional analogue of canonical connection defined by Ehresman-Libermann’s on the almost K ̈ahler manifolds. We call it the canonical connection on contact manifolds. Further from the canonical connection, we construct a Hermitian connection of the pull back bundle w^*\xi. In the sequential talk, I use this Hermitian connection to give a tensorial way to derive the exponential decay of pseudo-holomorphic curves with gradient bound. This is a joint work with Yong-Geun Oh.

Dongning Wang Quantum Cohomology Ring of Toric Orbifolds via Seidel Representation

Abstract:

We compute the Seidel elements for toric orbifolds, and use them to show that the quantum cohomology ring of toric orbifolds is isomorphic to the quotient of a polynomial ring generated over novikov ring by certain relations. This result is for all toric orbifolds. If the toric orbifold is Fano or Nef, then the isomorphism can be written down explicitly. This is a joint work with Hsian-Hua Tseng.

Yoosik Kim Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group

Abstract:

I will talk about spectral invariants, related invariants and area conjecture proposed by Prof. Oh in his paper: Spectral invariants, analysis of the Floer moduli space, and geometry of the Hamiltonian diffeomorphism group.

Yunfeng Jiang an introduction on the geometry of spin equations

Abstract:

I will talk about the recent progress on the study of witten equation, including the precise definition, the analysis especially the compactifications. abstract: witten equation,orbifold structure , compactifications

References:

http://arxiv.org/abs/1209.3045

http://arxiv.org/abs/0812.4781

Past Semesters

• Spring 2011 Symplectic Geometry Seminar
• Fall 2011 Symplectic Geometry Seminar
• Spring 2012 Symplectic Geometry Seminar