Last Update: June 15th, 2021

Junior Symplectic Geometry (Virtual) Seminar Schedule

Spring 2021

Time: Mondays, 4:15pm-5:30pm (Zürich time/CEST)

Place: Zoom Meeting Room

The meeting room opens at 4:05pm and closes at 5:30pm.

Structure of the seminar: Each seminar will consist of two 25min talks given by each speaker with a 10min break in between. The speakers of the seminar will introduce one (and in some days two distinct) concept(s) along with several related examples in symplectic/contact geometry/topology that they have been studying closely and/or lately. Masters and PhD students are particularly encouraged to join!

Please feel free to forward it to others potentially interested!

Organizers: Bahar Acu, Valentin Bosshard, Patricia Dietzsch, Alessio Pellegrini, and Jagna Wisniewska

Upcoming Talk

This seminar has ended for the semester.

Full Schedule

May 3, 2021, Monday

- Speakers: Patricia Dietzsch (ETHZ) and Valentin Bosshard (ETHZ)
- Title: Examples of Lagrangian cobordisms and cobordism groups
- 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.

- Notes: First Talk and Second Talk

May 10, 2021, Monday

- Speakers: Alessio Pellegrini (ETHZ) and Ana Zegarac (ETHZ)
- Title: Classical and Hamiltonian Lusternik-Schnirelmann Theory
- 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.

- Notes: First Talk and Second Talk

May 17, 2021, Monday

- Speakers: Giovanni Ambrosioni (ETHZ) and Carl Felix Waller (ETHZ)
- Title: A_infinity-algebras and immersed Floer homology
- 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.

- Notes: First Talk and Second Talk

May 24, 2021, Monday

- No Seminar (Whit Monday)

May 31, 2021, Monday

- Speakers: Bahar Acu (ETHZ) and Joël Beimler (ETHZ)
- Title: Open books, Lefschetz fibrations, and symplectic fillings
- 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.

- Notes: First Talk and Second Talk

Additional references:

- Contact geometry notes by Ko Honda
- Contact structures in dim 3 and symplectic fillings notes by Patrick Massot
- Contact geometry lecture notes by Steven Sivek
- Survey article on the topology of symplectic fillings of contact manifolds by Burak Özbağcı

June 7, 2021, Monday

- Speakers: Michael Vogel (ETHZ) and Jagna Wisniewska (ETHZ)
- Title: b-Contact Structures on Symplectic Hyperboloids
- 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.

- Notes: First Talk and Second Talk

June 14, 2021, Monday

- Speakers: Rui Mendonca Martins (ETHZ) and Jagna Wisniewska (ETHZ)
- Title: Liouville Sectors
- 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.

- Notes: First Talk and Second Talk

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You might also be interested in:

Virtual Kylerec Student Seminar: A graduate student learning seminar in symplectic and contact topology where talks are given by graduate students for graduate students