Symplectic Geometry Study Group
CUNY Graduate CenterSpring 2022
Friday, 10:00am-11:30am
Co-organized with Bart Van Steirteghem and David Pham
Our seminar will be online in the Fall semester 2021. One of the goals is to understand Gromov’s nonsqueezing theorem.
Please email Fei Ye for the meeting link if you are interested in attending the seminar.
Upcoming Seminars
Past Seminars
Date: May 13, 2022
Speaker: TBA
Title: Differential Topology 8
Abstract: We will watch the youtube videos https://www.youtube.com/watch?v=dGmk_t8xHHM&list=PLo4jXE-LdDTQIrmgxcuLO9w5n6AdiltQo and have discussions.
Date: May 6, 2022
Speaker: TBA
Title: Differential Topology 7
Abstract: We will watch the youtube videos https://www.youtube.com/watch?v=dGmk_t8xHHM&list=PLo4jXE-LdDTQIrmgxcuLO9w5n6AdiltQo and have discussions.
Date: April 29, 2022
Speaker: TBA
Title: Differential Topology 6
Abstract: We will watch the youtube videos https://www.youtube.com/watch?v=dGmk_t8xHHM&list=PLo4jXE-LdDTQIrmgxcuLO9w5n6AdiltQo and have discussions.
Date: April 15, 2022
Speaker: TBA
Title: Differential Topology 5
Abstract: We will watch the youtube videos https://www.youtube.com/watch?v=dGmk_t8xHHM&list=PLo4jXE-LdDTQIrmgxcuLO9w5n6AdiltQo and have discussions.
Date: April 8, 2022
Speaker: TBA
Title: Differential Topology 4
Abstract: We will watch the youtube videos https://www.youtube.com/watch?v=dGmk_t8xHHM&list=PLo4jXE-LdDTQIrmgxcuLO9w5n6AdiltQo and have discussions.
Date: April 1, 2022
Speaker: TBA
Title: Differential Topology 3
Abstract: We will watch the youtube videos https://www.youtube.com/watch?v=dGmk_t8xHHM&list=PLo4jXE-LdDTQIrmgxcuLO9w5n6AdiltQo and have discussions.
Date: March 25, 2022
Speaker: TBA
Title: Differential Topology 2
Abstract: We will watch the youtube videos https://www.youtube.com/watch?v=dGmk_t8xHHM&list=PLo4jXE-LdDTQIrmgxcuLO9w5n6AdiltQo and have discussions.
Date: March 18, 2022
Speaker: TBA
Title: Differential Topology 1
Abstract: We will watch the youtube videos https://www.youtube.com/watch?v=dGmk_t8xHHM&list=PLo4jXE-LdDTQIrmgxcuLO9w5n6AdiltQo and have discussions.
Date: March 11, 2022
Speaker: TBA
Title: Equivariant Symplectic Geometry 3
Abstract: We will watch the youtube video https://www.youtube.com/watch?v=tRGco2OIZiM and have discussions.
Date: March 4, 2022
Speaker: TBA
Title: Equivariant Symplectic Geometry 2
Abstract: We will watch the youtube video https://www.youtube.com/watch?v=tRGco2OIZiM and have discussions.
Date: February 25, 2022
Speaker: TBA
Title: Equivariant Symplectic Geometry 1
Abstract: We will watch the youtube video https://www.youtube.com/watch?v=tRGco2OIZiM and have discussions.
Date: February 18, 2022
Speaker: David Pham (QCC)
Title: A Short Introduction to Moment Map
Date: February 8, 2022
Speaker: David Pham (QCC)
Title: Organizational Meeting
Abstract: We will discuss what to learn and plan the seminars for this semester.
Date: November 11, 2021
Speaker: David Pham (QCC)
Title: The Lie group $\mathrm{Sp}(2n,\mathbb{R})$
Abstract: We review some results concerning the Lie group of symplectic matrices.
Date: October 21, 2021
Speaker: David Pham (QCC)
Title: 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. Following the talk there will be a free discussion.
Date: October 7, 2021
Speaker: Fei Ye (QCC)
Title: 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.
Date: September 23, 2021
Speaker: David Pham (QCC)
Title: 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.
Date: September 9, 2021
Speaker: David Pham (QCC)
Title: 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.