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Spring Semester 2023

Date / Time Speaker Title Location
14 March 2023
09:00-10:15 		Adrian Dawid
ETH Zurich, Switzerland
Dr. Alessio Pellegrini
ETH Zurich, Switzerland
Event Details

Junior Symplectic Geometry Seminar

Title The Abbondandolo-Schwarz Isomorphism
Speaker, Affiliation Adrian Dawid, ETH Zurich, Switzerland
Dr. Alessio Pellegrini, ETH Zurich, Switzerland
Date, Time 14 March 2023, 09:00-10:15
Location HG G 19.2
Abstract Following Abbondandolo and Schwarz, we present an explicit isomorphism between the Hamiltonian Floer homology of the cotangent bundle $T^*M$ of a compact orientable manifold $M$ and the singular homology of its free loop space $\mathcal{L}M$. In the first part of the talk, we show that for a special class of Lagrangians the Lagrangian action functional satisfies the Palais--Smale condition. This allows us to construct a genuine Morse complex for the Lagrangian action functional, which computes the singular homology of $\mathcal{L}M$ by another result of Abbondandolo and Majer. In the second half of the talk, we explain Abbondandolo and Schwarz' isomorphism between said Morse- and Floer complexes for a suitable choice of Lagrangians and Hamiltonians. The explicit nature of this isomorphism allows for a clear geometric understanding of the isomorphism and comes with nice properties such as action-preservation.
The Abbondandolo-Schwarz Isomorphismread_more
HG G 19.2
28 March 2023
09:00-10:15 		Reto Kaufmann
ETH Zurich, Switzerland
Rodrigo Casado Noguerales
ETH Zurich, Switzerland
Event Details

Junior Symplectic Geometry Seminar

Title Hamiltonian group actions and the Duistermaat-Heckman Theorem
Speaker, Affiliation Reto Kaufmann, ETH Zurich, Switzerland
Rodrigo Casado Noguerales, ETH Zurich, Switzerland
Date, Time 28 March 2023, 09:00-10:15
Location HG G 19.2
Abstract Symplectic reduction formalises the classical Noether principle concerning mechanical systems: given a symmetry group of dimension k acting on a system, there appear k preserved quantities in the time evolution of the system that enable to reduce the number of degrees of freedom of the phase space by 2k. The symplectic reduction of a symplectic manifold under a Hamiltonian group action gives rise to a reduced symplectic structure after taking the quotient of a fiber of the moment map over the action. The Duistermaat--Heckman Theorem assesses the relationship between different reduced spaces for a torus-action: close fibers are identified diffeomorphically and the reduced symplectic form of a reduced space depends linearly on the value of the moment map. In cohomology this linear coefficient is an invariant, characteristic class of the associated torus-bundle. This leads to the fact that the pushforward of the Liouville measure by the moment map is a piecewise polynomial multiple of the Lebesgue measure on the dual of the Lie algebra.
Assets First Talkfile_download
Hamiltonian group actions and the Duistermaat-Heckman Theoremread_more
HG G 19.2
4 April 2023
09:00-10:15 		Dr. Jean-Philippe Chassé
ETH Zurich, Switzerland
Event Details

Junior Symplectic Geometry Seminar

Title h-principles
Speaker, Affiliation Dr. Jean-Philippe Chassé, ETH Zurich, Switzerland
Date, Time 4 April 2023, 09:00-10:15
Location HG G 19.2
Abstract In this talk, I will review some basic facts on h-principles without assuming any prior knowledge. I will then explain how these results have a wide variety of applications, especially in symplectic and contact topology. In particular, they will allow us to fully classify Lagrangian immersions into C^n.
h-principlesread_more
HG G 19.2
16 May 2023
09:00-10:15 		Giovanni Ambrosioni
ETH Zurich, Switzerland
Valentin Bosshard
ETH Zurich, Switzerland
Event Details

Junior Symplectic Geometry Seminar

Title Generating and split-generating Fukaya categories
Speaker, Affiliation Giovanni Ambrosioni, ETH Zurich, Switzerland
Valentin Bosshard, ETH Zurich, Switzerland
Date, Time 16 May 2023, 09:00-10:15
Location HG G 19.2
Abstract Computing Floer homology can be hard, computing Fukaya categories harder. We will motivate why it is useful to find a (split-)generating subset of objects in Fukaya categories mainly based on examples. In particular, we discuss generation of the wrapped Fukaya category of a cotangent bundle and split-generation of the Fukaya category of the torus. Moreover, we present a split-generation criterion due to Abouzaid by first going back to a linear version of it due to Biran-Cornea.
Generating and split-generating Fukaya categoriesread_more
HG G 19.2
30 May 2023
09:00-10:15 		Dr. Patricia Dietzsch
ETH Zurich, Switzerland
Ana Zegarac
ETH Zurich, Switzerland
Event Details

Junior Symplectic Geometry Seminar

Title Hofer's distance to powers
Speaker, Affiliation Dr. Patricia Dietzsch, ETH Zurich, Switzerland
Ana Zegarac, ETH Zurich, Switzerland
Date, Time 30 May 2023, 09:00-10:15
Location HG G 19.2
Abstract Following Polterovich-Shelukhin, we discuss a beautiful application of persistent homology to Symplectic Geometry. The main result states that there exist Hamiltonian diffeomorphisms that are arbitrarily far away in Hofer's distance from full k-powers (k>=2). The method of proof is based on persistent Floer homology: starting from an intuitive constraint for full k-powers, one can use persistent Floer homology to construct a robust obstruction. This obstruction can then be used to show that for certain Hamiltonian diffeomorphisms, the distance from full k-powers is unbounded.
Hofer's distance to powersread_more
HG G 19.2
20 June 2023
10:30-11:30 		Adrian Dawid
ETH Zurich, Switzerland
Event Details

Junior Symplectic Geometry Seminar

Title Floer Barcode Growth of Dehn-Seidel Twists
Speaker, Affiliation Adrian Dawid, ETH Zurich, Switzerland
Date, Time 20 June 2023, 10:30-11:30
Location HG G 19.2
Abstract Recently, a relationship between the growth of persistence barcodes of certain Floer complexes and the volume entropy of Hamiltonian diffeomorphisms has been established by Cineli, Ginzburg and Gürel. We investigate slow growth invariants — analogues of entropy that measure polynomial instead of expnential growth — using their strategy. We establish a lower bound on the slow volume growth of a compactly supported exact symplectomorphism of a Liouville domain by the slow growth of certain Floer barcodes. We then explain that the lower bound on the slow volume growth of a Dehn-Seidel twist established by Frauenfelder and Schlenk can be seen in this framework. Further, we show some stability properties of the slow barcode and volume growth invariants under Hofer-small perturbations.
Floer Barcode Growth of Dehn-Seidel Twistsread_more
HG G 19.2
20 June 2023
13:30-14:30 		Dr. Yusuke Kawamoto
ETH Zurich, Switzerland
Event Details

Junior Symplectic Geometry Seminar

Title The Auroux-Kontsevich-Seidel Theorem
Speaker, Affiliation Dr. Yusuke Kawamoto, ETH Zurich, Switzerland
Date, Time 20 June 2023, 13:30-14:30
Location HG G 19.2
The Auroux-Kontsevich-Seidel Theorem
HG G 19.2

Archive: SS 24 AS 23 SS 23 AS 22 SS 21

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