# Spring 2012 Symplectic Geometry Seminar

Wednesday 2:15pm-4:30pm 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) |
---|---|---|---|

Feb. 8th | Lino | Title | |

Feb. 15th | Kaileung Chan | Title | |

Feb. 22st | Chit Ma | Title | |

Feb. 29th | Dongning Wang | Seidel elements and mirror transformations | |

March. 7th | Jie Zhao | Title | |

March. 14th | Peng Zhou | Title | |

March. 21th | Jae-ho Lee | Title | |

March. 28th | Dongning Wang | Proof of the Triviality Axiom and Composition Axiom of Seidel Representation | |

April. 11th | Cheol-Hyun Cho | Title | |

April. 18th | Louis Lau | Title | |

April. 25th | Erkao Bao | On the Fukaya categories of higher genus surfaces. |

## Abstracts

**Dongning Wang** *Seidel elements and mirror transformations*

Abstract:

I will talk about the following paper by Eduardo Gonzalez, Hiroshi Iritani:

Seidel elements and mirror transformations

http://arxiv.org/abs/1103.4171

**Dongning Wang** "Proof of the Triviality Axiom and Composition Axiom of Seidel Representation"

Abstract:

I will briefly review the definition of Seidel representation, then introduce parametrized group action, Kuranishi structure, equivariant Kuranishi structure and parametrized equivariant Kuranishi structure, and use these to prove the triviality axiom of Seidel representation. To prove the composition axiom, I will construct a Lefschetz fibration, then consider then moduli spaces this space and their Kuranishi structures. Finally, if time permitted, I will mention the extra ingredients needed for orbifold Seidel representation.

**Erkao Bao** *On the Fukaya categories of higher genus surfaces*

I will present Abouzaid's paper: http://arxiv.org/abs/math/0606598. In this paper he proved that the Grothendieck group of the derived Fukaya category of a surface [math]\displaystyle{ \Sigma }[/math] with Euler characteristic [math]\displaystyle{ \chi (\Sigma)\lt 0 }[/math] is isomorphic to [math]\displaystyle{ H_1(\Sigma,\mathbb{Z})\oplus {\mathbb{Z}/ \chi (\Sigma) \mathbb{Z}} \oplus \mathbb{R} }[/math].