Osaka City University Advanced Mathematical Institute
Summer School on Symplectic Geometry and Toric Topology
Osaka City University, Osaka, Japan
17 July - 27 July, 2007
Overview
Osaka City University Advanced Mathematical Institute is organizing a summer school on symplectic geometry and toric topology in July, 2007. The school will be aimed at graduate students and mathematicians who are interested in symplectic geometry and toric topology.
The school will plan two lecture courses and a seminar: one lecture course on group actions in symplectic geometry, the other lecture course on toric topology and its application to complex cobordism, and a seminar by participants. There are also talks about related topics.
This summer school is partially supported by The 21st Century COE Program at Osaka City University.
Lecture notes and pictures are available.
See here.
Organizers :
- Mikiya Masuda (Osaka City University), masuda at sci.osaka-cu.ac.jp
- Shintaro Kuroki (OCAMI), kuroki at sci.osaka-cu.ac.jp
- Takahiko Yoshida (the University of Tokyo), takahiko at ms.u-tokyo.ac.jp
Last updated: 21 July 2008
Two lecture courses: 17 - 27 July
- An introduction to symplectic geometry
Instructor : Megumi Harada (McMaster University)
Date : 17 (Tuesday) - 20 (Friday) and 23 (Monday) - 27 (Friday) July
Time : 9:30--11:30
Room : Dept. of Mathematics, Sci. Bldg., 3040
Abstract :
The intent of this series of lectures is two-fold: in the first week, we will provide a quick overview of equivariant symplectic geometry, starting at the very beginning (i.e. with the definition of a symplectic structure). In the second week, we will give a series of loosely connected expository overviews of some themes that consistently arise in current research in this field. The purpose is to familiarize the audience with the basic tools and language of the field.
Topics will include (time permitting): In the first week, we will discuss the definition of a symplectic structure, examples of symplectic manifolds, local normal forms, group actions, Hamiltonian actions, moment maps, symplectic quotients, and Delzant's construction of symplectic toric manifolds. In the second week, we will discuss equivariant cohomology and equivariant Morse theory, localization, moment graphs and GKM theory, Duistermaat-Heckman measure, Kirwan surjectivity. I hope to also discuss related quotient theories (e.g. Kahler and hyperKahler quotients), time permitting.
- Toric topology and complex cobordism
Instructor: Taras Panov (Moscow State University)
Date : 17 (Tuesday) - 20 (Friday) July
Time : 13:30--15:30 (13:00 -- 14:00 on 18 (Wednesday))
Room : Dept. of Mathematics, Sci. Bldg., 3040
Abstract : We plan to discuss how the ideas and methodology of Toric Topology can be applied to one of the classical subjects of algebraic topology: finding nice representatives in complex cobordism classes. Toric and quasitoric manifolds are the key players in the emerging field of Toric Topology, and they constitute a sufficiently wide class of stably complex manifolds to additively generate the whole complex cobordism ring.
In other words, every stably complex manifold is cobordant to a manifold with a nicely behaving torus action.
An informative setting for applications of toric topology to complex cobordism is provided by the combinatorial and convex-geometrical study of analogous polytopes. By way of application, we give an explicit construction of a quasitoric representative for every complex cobordism class as the quotient of a free torus action on a real quadratic complete intersection. The latter is a yet another disguise of the moment-angle manifold, another familiar object of toric topology.
We suggest a systematic description for omnioriented quasitoric manifolds in terms of combinatorial data, and explain the relationship with non-singular projective toric varieties (otherwise known as toric manifolds).
See also here.
Seminar
In the summer school, we plan a seminar. Everyone who is interested in the seminar is welcome.
Program of the seminar
- For speakers of the seminar : A blackboard, an OHP, and a projector are available. But, please prepare a computer by yourself if you will use a computer.
Related talks
- Colloquiums
Room : Dept. of Mathematics, Sci. Bldg., 3040
- 18 July (Wed), 16:30 - 17:30
Speaker : Dong Youp Suh (KAIST)
Title : On manifolds whose cohomologies determine homeomorphism types (or diffeomorphism types)?
- 25 July (Wed), 16:30 - 17:30
Speaker : Zhi Lü (Fudan University)
Title : Equivariant cohomology and analytic descriptions of ring isomorphisms (joint work with Bo Chen)
- Differential Geometry Seminar
Room : Dept. of Mathematics, Sci. Bldg., 3040
- 18 July (wed), 14:40 - 16:10
Speaker : Miyuki Koiso ( Dept. of Math., Nara Women's Univ. )
Title : Rolling construction of plane curves and its application to surface theory
Post-summer school information:
- Pictures are up and available.
- Lecture notes are up and available.