Symplectic Geometry Study Group
Fall 2021 – Spring 2022
CUNY Graduate CenterFridays, 10:00 AM – 11:30 AM (Online)
Co-organizers: Bart Van Steirteghem and David Pham
Please email Fei Ye for the meeting link if you are interested in attending the seminar.
May 13, 2022 — TBA
Differential Topology 8
Abstract
We will watch the YouTube videos https://www.youtube.com/watch?v=dGmk_t8xHHM&list=PLo4jXE-LdDTQIrmgxcuLO9w5n6AdiltQo and have discussions.
May 6, 2022 — TBA
Differential Topology 7
Abstract
We will watch the YouTube videos https://www.youtube.com/watch?v=dGmk_t8xHHM&list=PLo4jXE-LdDTQIrmgxcuLO9w5n6AdiltQo and have discussions.
April 29, 2022 — TBA
Differential Topology 6
Abstract
We will watch the YouTube videos https://www.youtube.com/watch?v=dGmk_t8xHHM&list=PLo4jXE-LdDTQIrmgxcuLO9w5n6AdiltQo and have discussions.
April 15, 2022 — TBA
Differential Topology 5
Abstract
We will watch the YouTube videos https://www.youtube.com/watch?v=dGmk_t8xHHM&list=PLo4jXE-LdDTQIrmgxcuLO9w5n6AdiltQo and have discussions.
April 8, 2022 — TBA
Differential Topology 4
Abstract
We will watch the YouTube videos https://www.youtube.com/watch?v=dGmk_t8xHHM&list=PLo4jXE-LdDTQIrmgxcuLO9w5n6AdiltQo and have discussions.
April 1, 2022 — TBA
Differential Topology 3
Abstract
We will watch the YouTube videos https://www.youtube.com/watch?v=dGmk_t8xHHM&list=PLo4jXE-LdDTQIrmgxcuLO9w5n6AdiltQo and have discussions.
March 25, 2022 — TBA
Differential Topology 2
Abstract
We will watch the YouTube videos https://www.youtube.com/watch?v=dGmk_t8xHHM&list=PLo4jXE-LdDTQIrmgxcuLO9w5n6AdiltQo and have discussions.
March 18, 2022 — TBA
Differential Topology 1
Abstract
We will watch the YouTube videos https://www.youtube.com/watch?v=dGmk_t8xHHM&list=PLo4jXE-LdDTQIrmgxcuLO9w5n6AdiltQo and have discussions.
March 11, 2022 — TBA
Equivariant Symplectic Geometry 3
Abstract
We will watch the YouTube video https://www.youtube.com/watch?v=tRGco2OIZiM and have discussions.
March 4, 2022 — TBA
Equivariant Symplectic Geometry 2
Abstract
We will watch the YouTube video https://www.youtube.com/watch?v=tRGco2OIZiM and have discussions.
February 25, 2022 — TBA
Equivariant Symplectic Geometry 1
Abstract
We will watch the YouTube video https://www.youtube.com/watch?v=tRGco2OIZiM and have discussions.
February 18, 2022 — David Pham (QCC)
A Short Introduction to Moment Map
February 11, 2022 — David Pham (QCC)
Organizational Meeting
Abstract
We will discuss what to learn and plan the seminars for this semester.
November 11, 2021 — David Pham (QCC)
The Lie Group $\mathrm{Sp}(2n,\mathbb{R})$
Abstract
We review some results concerning the Lie group of symplectic matrices.
October 21, 2021 — David Pham (QCC)
Neighborhood Theorem I
Abstract
I will prove a standard neighborhood theorem from symplectic geometry using Moser’s trick. Specifically, let $M$ be a manifold and let $Q$ be a submanifold of $M$. Suppose $\omega_0$ and $\omega_1$ are two symplectic forms on $M$ such that $\omega_0 = \omega_1$ on $TM|_Q$. I will show there exists an (open) neighborhood $W$ of $Q$ and a diffeomorphism $F: W \to W$ which is the identity on $Q$ and satisfies $F^*\omega_1=\omega_0$. In the special case where $Q$ is a point, we obtain Darboux’s theorem as a corollary.
October 7, 2021 — Fei Ye (QCC)
Hamiltonian and Symplectic Vector Fields
Abstract
In this talk, we will discuss relations between Hamiltonian and symplectic fields as well as their properties and applications.
September 23, 2021 — David Pham (QCC)
Moser’s Trick & Darboux’s Theorem
Abstract
In this talk, we will begin with a quick review of vector field flows and time-dependent vector fields which will serve as the necessary background for Moser’s trick. After covering Moser’s trick, we will use it to prove Darboux’s theorem. Darboux’s theorem is the statement that all symplectic manifolds of the same dimension are locally isomorphic. Hence, symplectic manifolds have no local invariants.
September 9, 2021 — David Pham (QCC)
Organization Meeting
Abstract
I will explain Gromov’s nonsqueezing theorem. We will plan the seminar and discuss topics and questions that we would like to study. Participants are encouraged to bring in their own research interests in symplectic geometry for discussion.