Symplectic Geometry Seminar: Difference between revisions
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'''Erkao Bao''' ''On the Fukaya categories of higher genus surfaces'' | '''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>\Sigma </math> with Euler characteristic <math>\chi (\Sigma)<0 </math> is isomorphic to <math> | 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>\Sigma </math> with Euler characteristic <math>\chi (\Sigma)<0 </math> is isomorphic to <math>H_1(\Sigma,\mathbb{Z})\oplus {\mathbb{Z}/ \chi \mathbb{Z}} \oplus \mathbb{R}</math>. | ||
==Past Semesters == | ==Past Semesters == | ||
*[[ Spring 2011 Symplectic Geometry Seminar]] | *[[ Spring 2011 Symplectic Geometry Seminar]] | ||
*[[ Fall 2011 Symplectic Geometry Seminar]] | *[[ Fall 2011 Symplectic Geometry Seminar]] | ||
Revision as of 03:52, 22 April 2012
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 \mathbb{Z}} \oplus \mathbb{R} }[/math].