Departement Mathematik

Junior symplectic geometry seminar

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Frühjahrssemester 2021

Datum / Zeit Referent:in Titel Ort
3. Mai 2021
16:15-17:30 		Dr. Patricia Dietzsch
ETH Zurich, Switzerland
Valentin Bosshard
ETH Zurich, Switzerland
Details

Junior Symplectic Geometry Seminar

Titel Examples of Lagrangian cobordisms and cobordism groups
Referent:in, Affiliation Dr. Patricia Dietzsch, ETH Zurich, Switzerland
Valentin Bosshard, ETH Zurich, Switzerland
Datum, Zeit 3. Mai 2021, 16:15-17:30
Ort Zoom
Abstract The geometry of a symplectic manifold is often studied by studying its Lagrangian submanifolds. In our talk, we consider the relation of Lagrangian cobordisms between Lagrangian submanifolds. In particular, we carefully define Lagrangian cobordisms and give the main examples (Lagrangian suspension and surgery cobordisms) along with some pictures. Lagrangian cobordisms induce an equivalence relation on the set of Lagrangian submanifolds. We indicate through examples how to classify all exact Lagrangian submanifolds of punctured Riemann surfaces up to Lagrangian cobordisms.
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Second Talkfile_download
Examples of Lagrangian cobordisms and cobordism groupsread_more
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10. Mai 2021
16:15-17:30 		Ana Zegarac
ETH Zurich, Switzerland
Dr. Alessio Pellegrini
ETH Zurich, Switzerland
Details

Junior Symplectic Geometry Seminar

Titel Classical and Hamiltonian Lusternik-Schnirelmann Theory
Referent:in, Affiliation Ana Zegarac, ETH Zurich, Switzerland
Dr. Alessio Pellegrini, ETH Zurich, Switzerland
Datum, Zeit 10. Mai 2021, 16:15-17:30
Ort Zoom
Abstract In the first talk, we cover the basics of the Lusternik-Schnirelmann (short LS) theory in the context of closed geodesics. The goal of this talk is to provide a partial proof of the existence of at least one closed geodesic on a compact Riemannian manifold, following Lusternik and Fet. In the second part we present a Hamiltonian version of LS theory by defining spectral invariants and then explain how these are related to classical LS Theory. Along the way, we define the Hofer-Zehnder capacity and show that the finiteness thereof has striking dynamical consequences. At the end, we will discuss a Theorem of Irie that asserts the finiteness of certain Hofer-Zehnder capacities using the machinery of spectral invariants.
Unterlagen First Talkfile_download
Second Talkfile_download
Classical and Hamiltonian Lusternik-Schnirelmann Theoryread_more
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17. Mai 2021
16:15-17:30 		Giovanni Ambrosioni
ETH Zurich, Switzerland
Carl Felix Waller
ETH Zurich, Switzerland
Details

Junior Symplectic Geometry Seminar

Titel A_infinity-algebras and immersed Floer homology
Referent:in, Affiliation Giovanni Ambrosioni, ETH Zurich, Switzerland
Carl Felix Waller, ETH Zurich, Switzerland
Datum, Zeit 17. Mai 2021, 16:15-17:30
Ort Zoom
Abstract We will discuss the topological origin of A_infinity-algebras by looking at loop spaces: The failure of the concatenation map to be associative can be measured in a rigorous way by an infinite sequence of higher homotopies. We will see how this allows us to recognise loop spaces and how it leads to the notion of A_infinity-algebras. In the second part we will introduce pearly Floer cohomology for certain exact Lagrangian immersions and provide some examples of computations. At the end, we will discuss the product structure on pearly cohomology and mention how to obtain an A_infinity-algebra associated to a Lagrangian immersion.
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Second Talkfile_download
A_infinity-algebras and immersed Floer homologyread_more
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24. Mai 2021
16:15-17:30
Details

Junior Symplectic Geometry Seminar

Titel no seminar (Pentecost Monday)
Referent:in, Affiliation
Datum, Zeit 24. Mai 2021, 16:15-17:30
Ort Zoom
no seminar (Pentecost Monday)
Zoom
31. Mai 2021
16:15-17:30 		Joël Beimler
ETH Zurich, Switzerland
Bahar Acu
ETH Zurich, Switzerland
Details

Junior Symplectic Geometry Seminar

Titel Open books, Lefschetz fibrations, and symplectic fillings
Referent:in, Affiliation Joël Beimler, ETH Zurich, Switzerland
Bahar Acu, ETH Zurich, Switzerland
Datum, Zeit 31. Mai 2021, 16:15-17:30
Ort Zoom
Abstract Open book decompositions have been a versatile tool in the study of contact manifolds and their topology. In addition to providing several examples and outlining fundamental results concerning these objects, we explain how they naturally arise in the context of Lefschetz fibrations in symplectic geometry. Another important notion in studying contact and symplectic geometry on a smooth manifold is symplectic fillability. In the second part of the talk, we will describe the interplay between open book decompositions and Lefschetz fibrations in the context of symplectic fillings.
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Second Talkfile_download
Open books, Lefschetz fibrations, and symplectic fillingsread_more
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7. Juni 2021
16:15-17:30 		Jagna Wisniewska
ETH Zurich, Switzerland
Michael Vogel
ETH Zurich, Switzerland
Details

Junior Symplectic Geometry Seminar

Titel b-Contact Structures on Symplectic Hyperboloids
Referent:in, Affiliation Jagna Wisniewska, ETH Zurich, Switzerland
Michael Vogel, ETH Zurich, Switzerland
Datum, Zeit 7. Juni 2021, 16:15-17:30
Ort Zoom
Abstract In recent year there have been several developments in the study of Reeb dynamics on non-compact hypersurfaces - on one hand the tools of b-symplectic and b-contact geometry, on the other hand the Rabinowitz Floer homology for tentacular hyperboloids. However, up to now it was not clear if those two methods are related. In our talk we will present the first result in establishing a link between those two settings. In other words, we will show how to use the McGeehe transformation to endow a certain class of symplectic hyperboloids with a b-contact structure.
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Second Talkfile_download
b-Contact Structures on Symplectic Hyperboloidsread_more
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14. Juni 2021
16:15-17:30 		Jagna Wisniewska
ETH Zurich, Switzerland
Rui Mendonca Martins
ETH Zurich, Switzerland
Details

Junior Symplectic Geometry Seminar

Titel Classical and Hamiltonian Lusternik-Schnirelmann Theory
Referent:in, Affiliation Jagna Wisniewska, ETH Zurich, Switzerland
Rui Mendonca Martins, ETH Zurich, Switzerland
Datum, Zeit 14. Juni 2021, 16:15-17:30
Ort Zoom
Abstract Liouville manifolds are a well known example of symplectic manifolds. In our talk we extend this definition to include manifolds with boundary and introduce a special example called the Liouville Sectors. Further on we will analyze and discuss the duality between the analytic and topological conditions describing Liouville Sectors. The talk is based on the work by Ganatra, Pardon, and Shende.
Unterlagen First Talkfile_download
Second Talkfile_download
Classical and Hamiltonian Lusternik-Schnirelmann Theoryread_more
Zoom

Archiv: FS 24 HS 23 FS 23 HS 22 FS 21

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