General Information

Seminar Class Name: Torus Actions on Symplecti Manifolds

Aims: This is a reading & discussing Class on the Michèle Audin’s book, Torus Actions on Symplectic Manifolds, including some basic aspects about the theory of Lie groups and their actions, the Toric groups actions on Symplectic manifolds, momentum maps, Morse theory for Hamiltonians and some others topics, in the first semester (2021 autumn) we will just finish the first 3 chapters, the rest parts will be going on through the next semester (2022 spring).

Main References: Michèle Audin, Torus Actions on Symplectic Manifolds, Birkäuser.

Time & Place: 8:30am-11:30am, every Wednesday (2021.Sep.5th-Christmass 2021), 8:30am-11:30am, every Friday (2022.Feb.28th-2022.Jul.12th), Room 510, department of mathematics

Titles & Speakers

Introduction: Symmetry in Symplecti Geometry

Speaker: Prof. Shanzhong Sun. Date: 1st week

Lie Groups Actions, Koszul’s Slice Theorem and Some Applications

Speaker: Zhiyuan Liu. Date: 2nd-3rd weeks

The Classification of Actions on Closed Surfaces, The Euler Number of -bundles and the Hopf Fibrations

Speaker: Wen Shen. Date: 4th-5th week

The Classification of Oriented Seifert 3-Manifolds

Speaker: Jia Fei. Date: 7th-8th week

The Symplectic Manifolds

Speaker: Jinghong Deng. Date: 9th-11th week

Hamiltonian Vector Fields, Poinsson Brackets, Hamiltonian Groups Actions, and the Moment Maps

Speaker: Zhengtong Xie. Date: 12th & 16th-17th Week

A Week for Exercises

Speaker: Linfang Hou. Date: 14th-15th week

Some Properties of Moment Maps

Speaker: Zhiyuan Liu. Date: 17th week

Symplectic Reductions and Symplectic Orbifolds

Speaker: Wen Shen. Date: March 4th-11th, 2022

Integrable Systems

Speaker: Dr. Chow Hongjie. Date:March 11th-18th, 2022

Exercises Week for Chapter III

Speaker: Linfang Hou. Date: March 25th, 2022

Almost Periodic Hamiltonians and Morse Functions

Speaker: Zhiyuan Liu. Date: April 1st, 2022

The Atiyah’s Convexity Theorem

Speakers: Sanghao Xing, Jinghong Deng & Jia Fei. Date : April 7th-April 24th.

The Delzent Theorem

Speaker: Wen Shen. Date: April 25th-May 9th.

Atiyah’s Convexity theorem for Kähler Case & Kushnirenko Theorem

Speaker: Linfang Hou. Date: May 16th

The Classification of Compact Connected Symplectic -Manifolds in Dimension 4

Speaker: Zhiyuan Liu. Date: May 23rd

A Week for Exercises in Chapter IV

Speakers: Linfang Hou, Wen Shen, Zhiyuan Liu. Date: May 30th

Connections on Principal Bundles and the Moduli Space

Speaker: Zhiyuan Liu. Date:June 6th

Poisson Structures on the Moduli Space of Flat Connections

Speaker: Dr.Chow Hongjie. Date: June 13th, June 20th

Goldmann’s Integrable Systems on the Moduli Space

Speaker: Linfang Hou. Date: June 27th

Milnor’s Constructions of Universal Bundle

Speaker: Jinghong Deng. Date: July 25th

Equivariant Cohomology and Euler Classes

Speaker: Zhiyuan Liu. Date: Aug.1st