Junior Symplectic Geometry Seminar

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Spring Semester 2021

Date / Time

Speaker

Title

Location

3 May 2021
16:15-17:30

Dr. Patricia Dietzsch
ETH Zurich, Switzerland
Valentin Bosshard
ETH Zurich, Switzerland

Event Details

Junior Symplectic Geometry Seminar

Title	Examples of Lagrangian cobordisms and cobordism groups
Speaker, Affiliation	Dr. Patricia Dietzsch, ETH Zurich, Switzerland Valentin Bosshard, ETH Zurich, Switzerland
Date, Time	3 May 2021, 16:15-17:30
Location	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.
Assets	First Talkfile_download Second Talkfile_download

Examples of Lagrangian cobordisms and cobordism groupsread_more

Zoom

10 May 2021
16:15-17:30

Ana Zegarac
ETH Zurich, Switzerland
Dr. Alessio Pellegrini
ETH Zurich, Switzerland

Event Details

Junior Symplectic Geometry Seminar

Title	Classical and Hamiltonian Lusternik-Schnirelmann Theory
Speaker, Affiliation	Ana Zegarac, ETH Zurich, Switzerland Dr. Alessio Pellegrini, ETH Zurich, Switzerland
Date, Time	10 May 2021, 16:15-17:30
Location	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.
Assets	First Talkfile_download Second Talkfile_download

Classical and Hamiltonian Lusternik-Schnirelmann Theoryread_more

Zoom

17 May 2021
16:15-17:30

Giovanni Ambrosioni
ETH Zurich, Switzerland
Carl Felix Waller
ETH Zurich, Switzerland

Event Details

Junior Symplectic Geometry Seminar

Title	A_infinity-algebras and immersed Floer homology
Speaker, Affiliation	Giovanni Ambrosioni, ETH Zurich, Switzerland Carl Felix Waller, ETH Zurich, Switzerland
Date, Time	17 May 2021, 16:15-17:30
Location	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.
Assets	First Talkfile_download Second Talkfile_download

A_infinity-algebras and immersed Floer homologyread_more

Zoom

24 May 2021
16:15-17:30

Event Details

Junior Symplectic Geometry Seminar

Title	no seminar (Pentecost Monday)
Speaker, Affiliation
Date, Time	24 May 2021, 16:15-17:30
Location	Zoom

no seminar (Pentecost Monday)

Zoom

31 May 2021
16:15-17:30

Joël Beimler
ETH Zurich, Switzerland
Bahar Acu
ETH Zurich, Switzerland

Event Details

Junior Symplectic Geometry Seminar

Title	Open books, Lefschetz fibrations, and symplectic fillings
Speaker, Affiliation	Joël Beimler, ETH Zurich, Switzerland Bahar Acu, ETH Zurich, Switzerland
Date, Time	31 May 2021, 16:15-17:30
Location	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.
Assets	First Talkfile_download Second Talkfile_download

Open books, Lefschetz fibrations, and symplectic fillingsread_more

Zoom

7 June 2021
16:15-17:30

Jagna Wisniewska
ETH Zurich, Switzerland
Michael Vogel
ETH Zurich, Switzerland

Event Details

Junior Symplectic Geometry Seminar

Title	b-Contact Structures on Symplectic Hyperboloids
Speaker, Affiliation	Jagna Wisniewska, ETH Zurich, Switzerland Michael Vogel, ETH Zurich, Switzerland
Date, Time	7 June 2021, 16:15-17:30
Location	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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b-Contact Structures on Symplectic Hyperboloidsread_more

Zoom

14 June 2021
16:15-17:30

Jagna Wisniewska
ETH Zurich, Switzerland
Rui Mendonca Martins
ETH Zurich, Switzerland

Event Details

Junior Symplectic Geometry Seminar

Title	Classical and Hamiltonian Lusternik-Schnirelmann Theory
Speaker, Affiliation	Jagna Wisniewska, ETH Zurich, Switzerland Rui Mendonca Martins, ETH Zurich, Switzerland
Date, Time	14 June 2021, 16:15-17:30
Location	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.
Assets	First Talkfile_download Second Talkfile_download

Classical and Hamiltonian Lusternik-Schnirelmann Theoryread_more

Zoom

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