Reading Seminar on Symplectic Geometry (summer semester 2021, HU Berlin)

Organizers: Shah Faisal and Naageswaran Manikandan

We aim to cover the contents of Lectures on Symplectic Geometry by Ana Cannas da Silva. The seminar can act as a prerequisite to advanced symplectic events that happen at HU. Our talks happen virtually via Zoom on Friday from 1:00 pm to 3:00 pm during the summer semester 2021 provided that it does not clash with the timing of the MATH+ Friday lectures. In case of a clash, we will shift the time only for that Friday. Any change will be communicated via email.

This seminar is organized by students for students. If you would like to attend or help with organizing or give a lecture on some topics of your choice from the lecture notes, please write to us at symplecticg@gmail.com.

Some prerequisites:

Smooth manifolds, Vector fields and their flows, Basics Riemannian geometry: Chapters in Differential Geometry: Connections, Curvature, and Characteristic Classes by Loring.
Differential Forms, De Rham Cohomology: Chapter 5, 6 in Introduction to differential topology by Salamon and Robbin.
Homology and cohomology: Topology I and II: Lecture notes by our Chris Wendl.

Schedule (download in pdf):

Talk 01 (First week of Summer semester 2021)
Topics: Symplectic Manifolds, Symplectomorphisms, Lagrangian Submanifolds of cotangent Bundle
Reference: Chapter 1,2 and 3 in Lectures on Symplectic Geometry .
Speaker: Yoanna Kirilova
When: 16.04.2021, 1:00-3:00 pm
Location: Via Zoom
Lecture Notes: click me

Talk 02
Topics: Generating Functions: Constructing Symplectomorphisms, Method of Generating Functions, Application to Geodesic Flow, Tubular Neighborhood Theorem.
Reference: Chapters 4, 5, and 6 in Lectures on Symplectic Geometry.
Speaker: Leo Mousseau
When: 23.04.2021, 1:00-3:00 pm
Location: Via Zoom
Lecture Notes: click me

Talk 03
Topics: Moser Trick and applications Part-I
Reference: Chapter 7, 8 and 9 in Lectures on Symplectic Geometry .
Speaker: Shah Faisal
When: 30.04.2021, 1:00-3:00 pm
Location: Via Zoom.
Lecture Notes: click me

Talk 04
Topics: Moser Trick and Applications Part-II
Reference: Chapter 7, 8 and 9 in Lectures on Symplectic Geometry .
Speaker: Shah Faisal
When: 07.05.2021, 3:00-5:00 pm
Location:Via Zoom
Lecture Notes: click me

Talk 05
Temporary Topics: Contact Structures, Reeb dynamics, Symplectization, Conjectures of Seifert and Weinstein
Reference: Chapters 10 and 11 in Lectures on Symplectic Geometry .
Speaker: David Suchodoll
When: 14.05.2021, 1:00-3:00 pm
Lecture Notes: click me

Talk 06
Temporary Topics: Almost Complex Structures, Compatible Triples
Reference: Chapters 12 and 13 in Lectures on Symplectic Geometry .
Speaker: Tim Sehiipferling
When: 21.05.2021, 3:00-5:00 pm
Lecture Notes: click me

Talk 07
Topics: Complex Manifolds, Dolbeault Cohomology
Reference: chapter 14 and 15 in Lectures on Symplectic Geometry .
Speaker: Adrian Philipp Dawid
When: 28.05.2021, 1:00-3:00 pm
Lecture Notes: click me

Talk 08
Topics: Kahler Manifolds
Reference: Chapters 16 and 17 in Lectures on Symplectic Geometry .
Speaker: Jacek Rzemieniecki
When: 04.06.2021, 1:00-3:00 pm
Lecture Notes: click me

Talk 09
Topics:: Hamiltonian and Symplectic Vector Fields, Brackets, Integrable Systems, Variational Principles.
Reference: Chapters 18, 19 and 20 in Lectures on Symplectic Geometry .
Speaker: Jonas Lautenschlager
When: 11.06.2021, 1:00-3:00 pm
Location: Zoom link

Talk 10
Topic: Moment Maps
Reference: Chapters 21 and 22 in Lectures on Symplectic Geometry .
Speaker: Naageswaran Manikandan
When: 18.06.2021, 1:00-3:00 pm
Lecture Notes: click me

Talk 11
Topic: Symplectic Reduction
Reference: Chapters 23 and 24 in Lectures on Symplectic Geometry .
Speaker: Paramjit Singh
When: 25.06.2021, 1:00-3:00 pm
Lecture Notes: click me

Talk 12
Topic: Symplectic Toric Manifolds
Reference: Chapters 28, 29, 30 in Lectures on Symplectic Geometry .
Speaker: Michael Rothgang
When: 07.02.2021, 1:00-3:00 pm
Location: Zoom link

Some other interesting events happening this semester:

(BMS advanced course) Differential Geometry IV by Professor Klaus Mohnke
(BMS advanced course) 4-Manifolds and Kirby calculus by Dr. Marc Kegel
(Seminar) Riemannian Convergence Theory by Professor Thomas Walpuski
(Seminar) h-Principle by Professor Klaus Mohnke
Augsburg-Berlin-Hamburg-Regensburg Seminar on Symplectic Geometry (One needs to login to moodle.hu-berlin.de)