# Fall 2012 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 | ||

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 compact 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