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Autumn Semester 2020

Date / Time Speaker Title Location
* 28 September 2020
16:10-17:20
Event Details

Symplectic Geometry Seminar

Title no semianr
Speaker, Affiliation
Date, Time 28 September 2020, 16:10-17:20
Location
no semianr
* 5 October 2020
16:10-17:20 		Jagna Wisniewska
ETH Zürich
Event Details

Symplectic Geometry Seminar

Title Weinstein conjecture for tentacular hyperboloids
Speaker, Affiliation Jagna Wisniewska, ETH Zürich
Date, Time 5 October 2020, 16:10-17:20
Location Link to recording of the talk (password: segtsh20)
Abstract Rabinowitz Floer homology is an algebraic invariant of contact-type hypersurfaces in exact symplectic manifolds. It captures the relation between closed solutions of Hamilton’s equations with a fixed energy and the geometry of the corresponding energy hypersurface. The Rabinowitz Floer homology was first defined for compact hypersurfaces and in this talk we will show how to extend it to include examples of non-compact hypersurfaces. We will also present computational results of Rabinowitz Floer homology for a class of hyperboloids and show how it can be used to prove the Weinstein conjecture.
Assets Link to previous recordings. Password: segtsh20file_download
Weinstein conjecture for tentacular hyperboloidsread_more
Link to recording of the talk (password: segtsh20)
* 12 October 2020
16:10-17:20 		Valentin Bosshard
ETH Zurich
Event Details

Symplectic Geometry Seminar

Title On Lagrangian Cobordisms in Liouville manifolds
Speaker, Affiliation Valentin Bosshard, ETH Zurich
Date, Time 12 October 2020, 16:10-17:20
Location Link to recording of the talk (password: segtsh20)
Abstract The theory of Lagrangian cobordisms was developed by Biran and Cornea to study the triangulated structure of the derived Fukaya category of monotone symplectic manifolds. Recent developments in the study of Liouville manifolds (mainly the GPS-papers) enable us to transfer the theory of Lagrangian cobordisms to Liouville manifolds and its derived Wrapped Fukaya category. We review the wrapped Fukaya category of a disk equipped with stops on its boundary and relate it to the theory of Lagrangian cobordism.  Furthermore, we compute the cobordism groups of non-compact Riemann surfaces of finite type.
Assets Link to previous recordings. Password: segtsh20file_download
On Lagrangian Cobordisms in Liouville manifoldsread_more
Link to recording of the talk (password: segtsh20)
* 19 October 2020
16:10-17:20 		Alessio Pellegrini
ETH
Event Details

Symplectic Geometry Seminar

Title Polytope Novikov Homology
Speaker, Affiliation Alessio Pellegrini, ETH
Date, Time 19 October 2020, 16:10-17:20
Location Link to recording of the talk (password: segtsh20)
Abstract Let $M$ be a closed manifold and $\mathcal{A}$ a polytope in the first de Rham cohomology group of $M$. For each cohomology class $a \in \mathcal{A}$ we define a Novikov chain complex with a multiple finiteness condition encoded by the polytope $\mathcal{A}$. The resulting polytope Novikov homology generalizes the ordinary Novikov homology. We prove that any two cohomology classes in a prescribed polytope give rise to chain homotopy equivalent polytope Novikov complexes over a Novikov ring associated to said polytope. As applications we present a novel approach to the (twisted) Novikov Morse Homology Theorem and prove a new polytope Novikov Principle, which generalizes a recent result of Pajitnov.
If time permits we will discuss the corresponding polytope Novikov-Floer analogue on Liouville domains.
Assets Link to previous recordings. Password: segtsh20file_download
Polytope Novikov Homologyread_more
Link to recording of the talk (password: segtsh20)
* 26 October 2020
16:10-17:20 		Joontae Kim
Korea Institute for Advanced Study (KIAS)
Event Details

Symplectic Geometry Seminar

Title Real Lagrangians in some symplectic 4-manifolds
Speaker, Affiliation Joontae Kim, Korea Institute for Advanced Study (KIAS)
Date, Time 26 October 2020, 16:10-17:20
Location Link to recording of the talk (password: segtsh20)
Abstract We are interested in a class more rigid than monotone Lagrangians, namely real Lagrangians. A real Lagrangian in a symplectic manifold is the fixed point set of an antisymplectic involution. We study the classification problem of real Lagrangians in monotone symplectic 4-manifolds. In particular, we give the complete answer in case of $CP^2$ and $S^2\times S^2$. The talk is partly based on work of Joé Brendel and Jiyeon Moon.
Assets Link to previous recordings. Password: segtsh20file_download
Real Lagrangians in some symplectic 4-manifoldsread_more
Link to recording of the talk (password: segtsh20)
* 2 November 2020
15:00-16:00 		Shira Tanny
Tel-Aviv University
Event Details

Symplectic Geometry Seminar

Title The Poisson bracket invariant: soft and hard approaches
Speaker, Affiliation Shira Tanny, Tel-Aviv University
Date, Time 2 November 2020, 15:00-16:00
Location Link to recording of the talk (password: segtsh20)
Abstract In 2006 Entov and Polterovich proved that functions forming a partition of unity with displaceable supports cannot commute with respect to the Poisson bracket. In 2012 Polterovich conjectured a quantitative version of this theorem. I will discuss three interconnected topics: a solution of this conjecture in dimension two (with Lev Buhovsky and Alexander Logunov), a link between this problem and Grothendieck's theorem from functional analysis (with Efim Gluskin), and new results related to the Floer-theoretical approach to this conjecture (with Yaniv Ganor).
Assets Link to recording of the talk (password: segtsh20)file_download
The Poisson bracket invariant: soft and hard approachesread_more
Link to recording of the talk (password: segtsh20)
* 2 November 2020
16:10-17:20 		Igor Uljarevic
University of Belgrade
Event Details

Symplectic Geometry Seminar

Title Exotic symplectomorphisms and contact circle actions
Speaker, Affiliation Igor Uljarevic, University of Belgrade
Date, Time 2 November 2020, 16:10-17:20
Location Link to recording of the talk (password: segtsh20)
Abstract An exotic symplectomorphism is a symplectomorphism that is not isotopic to the identity through compactly supported symplectomorphisms. Using Floer-theoretic methods, we prove that the non-existence of an exotic symplectomorphism on the standard symplectic ball implies a rather strict topological condition on the free contact circle actions on the boundary sphere. We also prove an analogue for a Liouville domain and contact circle actions on its boundary. Applications include results on the symplectic mapping class group, the fundamental group of the group of contactomorphisms, and exotic contact structures on the 3-sphere. The talk is based on joint work with Dusan Drobnjak.
Assets Link to recording of the talk (password: segtsh20)file_download
Exotic symplectomorphisms and contact circle actionsread_more
Link to recording of the talk (password: segtsh20)
* 9 November 2020
16:10-17:20 		Gleb Smirnov
ETH Zürich
Event Details

Symplectic Geometry Seminar

Title Symplectic topology of K3 surfaces via Seiberg-Witten invariants
Speaker, Affiliation Gleb Smirnov, ETH Zürich
Date, Time 9 November 2020, 16:10-17:20
Location
Abstract We will show that the Torelli symplectic mapping class group of a generic K3 is "big" in the sense that it contains an infinitely-generated subgroup.
Symplectic topology of K3 surfaces via Seiberg-Witten invariantsread_more
* 23 November 2020
15:00-16:00 		Bahar Acu
ETH Zürich
Event Details

Symplectic Geometry Seminar

Title Talk 1: Generalizations of planar contact manifolds to higher dimensions
Speaker, Affiliation Bahar Acu, ETH Zürich
Date, Time 23 November 2020, 15:00-16:00
Location
Abstract In this talk, I will report on the progress made on the talk I gave here in Fall 2019. We will start with some background on "iterated planar contact manifolds" and discuss several examples and constructions showing that many contact manifolds are iterated planar. We will also introduce projective contact manifolds, another generalization of planar contact manifolds to higher dimensions, and show that some projective contact manifolds admit explicit symplectic caps. This is joint work with J. Etnyre and B. Özbağcı.
Talk 1: Generalizations of planar contact manifolds to higher dimensionsread_more
* 23 November 2020
16:15-17:25 		Silvia Anjos
Instituto Superior Técnico, Portugal
Event Details

Symplectic Geometry Seminar

Title Talk 2: Loops in the fundamental group of $\mathrm{Symp}(M,\omega)$ which are not represented by circle actions
Speaker, Affiliation Silvia Anjos, Instituto Superior Técnico, Portugal
Date, Time 23 November 2020, 16:15-17:25
Location Link to recording of the talk (password: segtsh20)
Abstract It was observed by J. K\c{e}dra that there are many symplectic 4-manifolds $(M, \omega)$, where $M$ is neither rational nor ruled, that admit no circle action and $\pi_1 (\mathrm{Ham}( M))$ is nontrivial. In the case $M={\mathbb C\mathbb P}^2\#\,k\overline{\mathbb C\mathbb P}\,\!^2$, with $k \leq 4$, it follows from the work of several authors that the full rational homotopy of $\mathrm{Symp}(M,\omega)$, and in particular their fundamental group, is generated by circle actions on the manifold. In this talk we study loops in the fundamental group of $\mathrm{Symp}_h({\mathbb C\mathbb P}^2\#\,5\overline{\mathbb C\mathbb P}\,\!^2) $ of symplectomorphisms that act trivially on homology, and show that, for some particular symplectic forms, there are loops which cannot be realized by circle actions. Our work depends on Delzant classification of toric symplectic manifolds and Karshon's classification of Hamiltonian circle actions.
Assets Link to recording of the talk (password: segtsh20)file_download
Talk 2: Loops in the fundamental group of $\mathrm{Symp}(M,\omega)$ which are not represented by circle actionsread_more
Link to recording of the talk (password: segtsh20)
* 30 November 2020
16:10-17:20 		Sobhan Seyfaddini
Institut de Mathématiques de Jussieu, Paris
Event Details

Symplectic Geometry Seminar

Title The large-scale geometry of Hofer's metric
Speaker, Affiliation Sobhan Seyfaddini, Institut de Mathématiques de Jussieu, Paris
Date, Time 30 November 2020, 16:10-17:20
Location Link to recording of the talk (password: segtsh20)
Abstract The main theme of this talk will be the large-scale geometry of Hofer's celebrated metric. This is a subject which has been studied extensively since the 90s and has seen much progress for a large class of symplectic manifolds. However, the case of the two-sphere has remained very mysterious, especially in comparison to other surfaces. We will discuss a well-known conjecture of Kapovich and Polterovich, from 2006, stating that, on the two-sphere, Hofer's metric is not quasi-isometric to the real line. The same question is known, in the affirmative, for many symplectic manifolds including all other surfaces. This is based on joint work with Dan Cristofaro-Gardiner and Vincent Humilière.
Assets https://polybox.ethz.ch/index.php/s/xZxGnAiL84PQm3kfile_download
The large-scale geometry of Hofer's metricread_more
Link to recording of the talk (password: segtsh20)
* 7 December 2020
16:10-17:20 		Nick Sheridan
University of Edinburgh
Event Details

Symplectic Geometry Seminar

Title Quantum cohomology as a deformation of symplectic cohomology
Speaker, Affiliation Nick Sheridan, University of Edinburgh
Date, Time 7 December 2020, 16:10-17:20
Location Link to recording of the talk (password: segtsh20)
Abstract Let X be a compact symplectic manifold, and D a normal crossings symplectic divisor in X. We give a criterion under which the quantum cohomology of X is the cohomology of a natural deformation of the symplectic cochain complex of X \ D. The criterion can be thought of in terms of the Kodaira dimension of X (which should be non-positive), and the log Kodaira dimension of X \ D (which should be non-negative). This is joint work with Strom Borman and Umut Varolgunes.
Assets Link to recording of the talk (password: segtsh20)file_download
Quantum cohomology as a deformation of symplectic cohomologyread_more
Link to recording of the talk (password: segtsh20)
* 14 December 2020
16:10-17:20
Event Details

Symplectic Geometry Seminar

Title no seminar
Speaker, Affiliation
Date, Time 14 December 2020, 16:10-17:20
Location
no seminar

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