Gökova Geometry Topology Institute

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**Date:** August 23-26, 2021

**Speakers:** Joé Brendel (University of Neuchâtel) and Felix Schlenk (University of Neuchâtel)

**Title:** Toric Symplectic Manifolds

**Abstract:** Toric symplectic manifolds are symplectic manifolds with an effective Hamiltonian torus action of maximal dimension. Toric manifolds are distinguished by the property that they can be reconstructed from a combinatorial object called the moment polytope. Thus they are a great playground for symplectic topology and the study of Lagrangian submanifolds, since complicated invariants may be reduced to combinatorial properties of the corresponding moment polytope. In recent years, there has been much interest in a generalization called "almost toric" structures. 

In these four lectures, we will introduce these two classes of symplectic manifolds, and use their special structure to study Lagrangian tori and symplectic embedding problems.
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**Slack workspace [[https://join.slack.com/t/ggtiworkspace/shared_invite/zt-tjxz56ie-vl5JfDMT2Nq~ve9NrCH3HQ|link]]** for discussions. (Let us know if the link is expired.)

**Lecture 1.** Monday, August 23 at 6 AM (PT), 9 AM (EDT), 4 PM (TRT)

The Delzant construction by **Joé Brendel** 
  * [[https://youtu.be/6YYLg3oQpGY|Lecture Video]]
  * {{ :lecture:2021:joe-lecture-1-and-exercises.pdf |Lecture Note with Exercises}}
  * {{ :lecture:2021:joe-lecture-1-extras.pdf |Extras}}

**Lecture 2.** Tuesday, August 24 at 6 AM (PT), 9 AM (EDT), 4 PM (TRT)

Versal deformations and the Chekanov torus by **Joé Brendel**
  * [[https://www.youtube.com/watch?v=qAniIt2j-AM|Lecture Video]]
  * {{ :lecture:2021:joe-lecture-2.pdf|Lecture Note}}

**Zoom Meeting ID** 936 2425 0802

**Password** Initials of the speaker's name (use capitals)

** Şifre** Konuşmacının adının baş harfleri (büyük harflerle)

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**Lecture 3.** Wednesday, August 25 at 6 AM (PT), 9 AM (EDT), 4 PM (TRT)

Almost toric symplectic fibrations by **Felix Schlenk**
  * [[http://www.youtube.com/watch?v=W1b2K_xwasM|Lecture Video]]


**Lecture 4.** Thursday, August 26 at 6 AM (PT), 9 AM (EDT), 4 PM (TRT)

Three applications (maximal embeddings of ellipsoids, exotic Lagrangian tori, and non-isotopic cube embeddings) by **Felix Schlenk**
  * [[https://www.youtube.com/watch?v=QsgyUX-zHwg|Lecture Video]]
  * {{ :lecture:2021: felix-schlenk-lectures.pdf |Lecture Notes (1-2)}}



**Zoom Meeting ID** 992 2975 8990

**Password** Initials of the speaker's name (use capitals)

** Şifre** Konuşmacının adının baş harfleri (büyük harflerle)
Gökova Geometry Topology Institute

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