## Western Hemisphere Virtual Symplectic Seminar (WHVSS)

## Fall 2022

**Mission Statement**

**Mission Statement**

**The mission of the WHVSS is to increase access to mathematical research and disseminate recent results in a collegial and respectful environment.**

**The mission of the WHVSS is to increase access to mathematical research and disseminate recent results in a collegial and respectful environment.**

**Please suggest your thesis students with current research ****here**** ****as speakers, or any other speakers you recommend.**

**Please suggest your thesis students with current research**

**here**

**as speakers, or any other speakers you recommend.**

**Logistics**

**Logistics**

**Organizers**

**Organizers**

Mohammed Abouzaid (Columbia), Nate Bottman (Max Planck),

Catherine Cannizzo (UC Riverside), Sheel Ganatra (USC), Kyler Siegel (USC)

**Schedule and Zoom info**

**Schedule and Zoom info**

In Fall 2022, our seminar meets online Fridays at 1 pm ET.

Zoom Link: https://columbiauniversity.zoom.us/j/96547665252?pwd=T0pOb28vM2JJSnRYM2RjeFBhWU96QT09

Meeting ID: 965 4766 5252 Passcode: 310229

One tap mobile: +16694449171, 96547665252#,*310229# US

Zoom meetings open 15 minutes before the talk begins.

Talks are 50 minutes, followed by a 10 min Q&A and an informal discussion session.

Preceding the talk, we will host an informal symplectic tea each Friday on gather.town from 12:45 pm - 1 pm ET at the following URL: https://gather.town/app/abBT3vhSL9vD0zbL/virtualsymplectictea

To receive announcements of talks, please join our email listerv.

**Notes and Videos**

**Notes and Videos**

**Speaker ****suggestions**

**Speaker**

**suggestions**

https://forms.gle/fnBvwohDHFPK5Qfc6

**F****eedback s****urvey**** about the seminar**

**F**

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**about the seminar**

**Speaker titles and abstracts**

**Speaker titles and abstracts**

**September 2****, 1 pm ET: ****Ipsita Datta**** (****Institute for Advanced Study****) - Lagrangian cobordisms, enriched knot diagrams, and algebraic invariants**

**September 2**

**, 1 pm ET:**

**Ipsita Datta**

**(**

**Institute for Advanced Study**

**) - Lagrangian cobordisms, enriched knot diagrams, and algebraic invariants**

Abstract: We introduce new invariants to the existence of Lagrangian cobordisms in R^4. These are obtained by studying holomorphic disks with corners on Lagrangian tangles, which are Lagrangian cobordisms with flat, immersed boundaries.

We develop appropriate sign conventions and results to characterize boundary points of 1-dimensional moduli spaces with boundaries on Lagrangian tangles. We then use these to define (SFT-like) algebraic structures that recover the previously described obstructions.

This talk is based on my thesis work under the supervision of Y. Eliashberg and on work in progress joint with J. Sabloff.

**September ****23****, 1 pm ET: ****Bingyu Zhang**** (****University of Southern Denmark****) ****- Circle Action of Microlocal Kernels**

**September**

**23**

**, 1 pm ET:**

**Bingyu Zhang**

**(**

**University of Southern Denmark**

**)**

**- Circle Action of Microlocal Kernels**

Abstract: The sheaf theoretical proof of the contact non-squeezing theorem relies on a $\mathbb{Z}/\ell$-equivariant invariant constructed using microlocal kernels of balls. We call it the ($\mathbb{Z}/\ell$- equivariant-)Chiu-Tamarkin complex. Chiu uses a numerical way to approximate $S^1$ in his proof. Later, his idea is packed as some symplectic/contact capacities by me. However, it is interesting to know if we can construct an $S^1$ action directly and algebraically. In this talk, I will explain how we build an $S^1$ action using the simplest property of the microlocal kernel. Then we can define the $S^1$-equivariant Chiu-Tamarkin complex. If time permits, I will also explain some computational results.

**September ****30****, 1 pm ET: ****Rohil Prasad**** (****Princeton****) - A strong closing lemma for ellipsoids**

**September**

**30**

**, 1 pm ET:**

**Rohil Prasad**

**(**

**Princeton**

**) - A strong closing lemma for ellipsoids**

Abstract: In a recent preprint, Irie conjectured a "strong closing property" for the Reeb flow on the boundary of any ellipsoid. This conjecture asserts that a Reeb orbit can be created in any open set by a C^\infty-small compactly supported perturbation of the contact form. In this talk, I will explain a proof of this conjecture, which uses spectral invariants from contact homology and higher-dimensional holomorphic intersection theory. This is joint work with J. Chaidez, I. Datta, and S. Tanny.

**October 7****, 1 pm ET: ****Luya Wang**** (****UC Berkeley****) - ****A connected sum formula of embedded contact homology**

**October 7**

**, 1 pm ET:**

**Luya Wang**

**(**

**UC Berkeley**

**) -**

**A connected sum formula of embedded contact homology**

Abstract: The contact connected sum is a well-understood operation for contact manifolds. I will focus on the 3-dimensional case where the contact connected sum can be seen as a Weinstein 1-handle attachment. I will discuss how pseudo-holomorphic curves in the symplectization behave under this operation, and as a result a connected sum formula of embedded contact homology.

**October ****14****, 1 pm ET: ****Maxim Jeffs (Harvard)**** - ****Functoriality for Fukaya categories of very affine hypersurfaces**

**October**

**14**

**, 1 pm ET:**

**Maxim Jeffs (Harvard)**

**-**

**Functoriality for Fukaya categories of very affine hypersurfaces**

Abstract: A very affine hypersurface is the vanishing locus of a Laurent polynomial inside a complex torus; its complement is also a very affine hypersurface, in one of two subtly-different ways. The (partially) wrapped Fukaya categories of the hypersurface and its complement are closely related: Auroux sketched the definitions of several new acceleration and restriction functors between them. I'll explain how we can define these functors in terms of gluings of Liouville sectors and how this implies conjectures of Auroux about their mirror counterparts, building on work of Gammage-Shende. On the way, I'll explain how the different realizations of the complement lead to very different Fukaya categories, related by a non-geometric equivalence mediated by derived Knorrer periodicity. This is joint work with Benjamin Gammage.

**October ****21****, 1 pm ET: ****Kai Hugtenburg (Edinburgh) ****- ****The cyclic open-closed map, u-connections and R-matrices**

**October**

**21**

**, 1 pm ET:**

**Kai Hugtenburg (Edinburgh)**

**-**

**The cyclic open-closed map, u-connections and R-matrices**

Abstract: This talk will review recent progress on obtaining Gromov-Witten invariants from the Fukaya category. A crucial ingredient is showing that the cyclic open-closed map, which maps the cyclic homology of the Fukaya category of X to its S1-equivariant quantum cohomology, respects connections. Along the way we will encounter R-matrices, which were used in the Givental-Teleman classification of semisimple cohomological field theories, and allow one to determine higher genus Gromov-Witten invariants from genus 0 invariants. I will then present some evidence that this approach might extend beyond the semisimple case. Time permitting, I will also explain work in progress on obtaining open Gromov-Witten invariants from the Fukaya category.

**October 2****8****, 1 pm ET:**** Yash Deshmukh ****(****Columbia****) - ****A homotopical description of Deligne-Mumford compactifications**

**October 2**

**8**

**, 1 pm ET:**

**Yash Deshmukh**

**(**

**Columbia**

**) -**

**A homotopical description of Deligne-Mumford compactifications**

Abstract: I will describe how the Deligne-Mumford compactifications of moduli spaces of curves (of all genera) arise from the moduli spaces of framed curves by homotopically trivializing certain circle actions in an appropriate sense. I will sketch how such a description is relevant to the problem of relating GW invariants (in all genera) with Fukaya categories. Finally, I will indicate how our result relates to other statements available in the literature. Time permitting, I will talk about a variation on this result which gives rise to a partial compactification of moduli spaces of curves which is relevant to the study of symplectic cohomology.

**November 11****, 1 pm ET: ****Yuan Yao**** (****UC Berkeley****) - ****Computing Embedded Contact Homology in the Morse-Bott Setting using Cascades**

**November 11**

**, 1 pm ET:**

**Yuan Yao**

**(**

**UC Berkeley**

**) -**

**Computing Embedded Contact Homology in the Morse-Bott Setting using Cascades**

Abstract: I will first give an overview of ECH. Then I will describe how to compute ECH in the Morse-Bott setting a la Bourgeois. I will discuss some classes of examples where this approach works. Finally I will sketch the gluing results that allow us to compute ECH using cascades.

**December 2****, 1 pm ET: ****Lea Kenigsberg ****(****Columbia****) - ****TBA**

**December 2**

**, 1 pm ET:**

**Lea Kenigsberg**

**(**

**Columbia**

**) -**

**TBA**

Abstract: TBA

**December ****16****, 1 pm ET: ****Debtanu Sen**** (****University of Southern California****) - TBA**

**December**

**16**

**, 1 pm ET:**

**Debtanu Sen**

**(**

**University of Southern California**

**) - TBA**

Abstract: TBA

**WHVSS weekly tea**

**WHVSS weekly tea**

Preceding the talk, we will host an informal symplectic tea each Friday on gather.town from 12:45 pm - 1 pm ET at the following URL:

https://gather.town/app/abBT3vhSL9vD0zbL/virtualsymplectictea

For those of you who haven't used it, gather.town simulates the experience of a large group gathering by allowing you to "walk up to people" in its interface and video chat with the people you are close to.

We are looking forward to seeing you there!