Junior Symplectic Geometry Seminar

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Autumn Semester 2022

Date / Time

Speaker

Title

Location

6 October 2022
14:15-15:30

Dr. Patricia Dietzsch
ETH Zurich, Switzerland
Adrian Dawid
ETH Zurich, Switzerland

Event Details

Junior Symplectic Geometry Seminar

Title	Persistence homology
Speaker, Affiliation	Dr. Patricia Dietzsch, ETH Zurich, Switzerland Adrian Dawid, ETH Zurich, Switzerland
Date, Time	6 October 2022, 14:15-15:30
Location	HG E 22
Abstract	Persistence homology is a widely known tool from topological data analysis (TDA), which is nowadays successfully applied in symplectic topology. In the first part of the talk, we introduce the concept of persistence modules, motivated from the perspective of TDA. We explain how the structure theorem for persistence modules gives rise to barcodes and compute the barcode of the Morse persistence homology of a concrete Morse function. The second speaker will then apply these concepts to the framework of Floer homology. We introduce a natural filtration on the Floer complex. This gives Floer homology the structure of a persistence module. We further see how spectral invariants can be interpreted as the endpoints of infinite bars in the barcode in this context. Lastly, we explain some stability properties of the Floer barcode under small perturbations of the data.
Assets	Second Talkfile_download

Persistence homologyread_more

HG E 22

20 October 2022
14:15-15:30

Dr. Yusuke Kawamoto
ETH Zurich, Switzerland

Event Details

Junior Symplectic Geometry Seminar

Title	Superpotentials for the applied symplectic geometer
Speaker, Affiliation	Dr. Yusuke Kawamoto, ETH Zurich, Switzerland
Date, Time	20 October 2022, 14:15-15:30
Location	HG E 22
Abstract	The superpotential of a Lagrangian L is a certain count of Maslov 2-disks on L. In this talk, we will see how superpotentials can be practically used for 1. computationing Floer homology of L, 2. distinguishing Lagrangians up to Hamiltonian isotopy. No background required (we will start by reviewing Floer homology and some fundamentals about Lagrangians).
Assets	Talkfile_download

Superpotentials for the applied symplectic geometerread_more

HG E 22

3 November 2022
14:15-15:30

Reto Kaufmann
ETH Zurich, Switzerland
Giovanni Ambrosioni
ETH Zurich, Switzerland

Event Details

Junior Symplectic Geometry Seminar

Title	Morse-Bott Functions from Moment Maps
Speaker, Affiliation	Reto Kaufmann, ETH Zurich, Switzerland Giovanni Ambrosioni, ETH Zurich, Switzerland
Date, Time	3 November 2022, 14:15-15:30
Location	HG E 22
Abstract	We will introduce the concept of Hamiltonian spaces and using the toric Darboux theorem we will show that moment maps are a rich source of Morse-Bott functions. As an application we will present how these Morse-Bott functions can be used in the study of recursive properties of symplectic toric manifolds.
Assets	Second Talkfile_download

Morse-Bott Functions from Moment Mapsread_more

HG E 22

10 November 2022
15:00-16:15

Valentin Bosshard
ETH Zurich, Switzerland

Event Details

Junior Symplectic Geometry Seminar

Title	The topological Fukaya category
Speaker, Affiliation	Valentin Bosshard, ETH Zurich, Switzerland
Date, Time	10 November 2022, 15:00-16:15
Location	ML F 36
Abstract	Kontsevich conjectured that the Fukaya category of a Stein manifold can be locally computed on a (singular) Lagrangian core. The talk will focus on why this result is true in dimension 2, where the statement reads as: The Fukaya category of a marked surface can be locally computed on a ribbon graph. Along the way we pick up easy examples of A_infinity categories, the notion of exact triangles and a topological/combinatorial construction of the Fukaya category. The main reference is Haiden, Katzarkov and Kontsevich.
Assets	Talkfile_download

The topological Fukaya categoryread_more

ML F 36

1 December 2022
15:00-16:15

Dr. Alessio Pellegrini
ETH Zurich, Switzerland

Event Details

Junior Symplectic Geometry Seminar

Title	Novikov-Floer Homology
Speaker, Affiliation	Dr. Alessio Pellegrini, ETH Zurich, Switzerland
Date, Time	1 December 2022, 15:00-16:15
Location	HF F 26.1
Abstract	In this talk, we explain how Novikov homology naturally arises as a generalization of Morse homology. After some computations, we will explain how the extension of Floer homology to non-Hamiltonian symplectic isotopies fits within the general framework of Novikov theory with respect to the flux of the isotopy. At the end, we present some basic facts that will be needed for the proof of the Flux Conjecture next week.

Novikov-Floer Homologyread_more

HF F 26.1

8 December 2022
15:00-16:15

Dr. Jean-Philippe Chassé
ETH Zurich, Switzerland

Event Details

Junior Symplectic Geometry Seminar

Title	The C1 Flux Conjecture
Speaker, Affiliation	Dr. Jean-Philippe Chassé, ETH Zurich, Switzerland
Date, Time	8 December 2022, 15:00-16:15
Location	HG F 26.1
Abstract	It is a natural question to ask how the group of Hamiltonian diffeomorphisms of a given symplectic manifolds sits inside the group of its symplectomorphisms. This question is however in general hard to answer, as we are dealing with infinite-dimensional Lie groups that have many natural choices of topologies. The C^1 flux conjecture states that the former group is closed in the latter in the C^1 topology. In this talk, I will present some background on the C^1 flux conjecture and explain Ono's proof of it using Novikov-Floer homology. This technical tool—originally introduced by Lê and Ono—gives a Floer homology theory for general symplectic isotopies by using the ideas of Novikov homology for a closed 1-form in the symplectic context.
Assets	Talkfile_download

The C1 Flux Conjectureread_more

HG F 26.1

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