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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
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.
Documents Second Talkfile_download
Persistence homologyread_more
HG E 22
20 October 2022
14:15-15:30 		Dr. Yusuke Kawamoto
ETH Zurich, Switzerland
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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).
Documents 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
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.
Documents 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
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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.
Documents Talkfile_download
The topological Fukaya categoryread_more
ML F 36
1 December 2022
15:00-16:15 		Dr. Alessio Pellegrini
ETH Zurich, Switzerland
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
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.
Documents Talkfile_download
The C1 Flux Conjectureread_more
HG F 26.1

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

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