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Autumn Semester 2024

Date / Time Speaker Title Location
* 23 September 2024
15:15-16:30 		Oliver Edtmair
ETH
Details

Symplectic Geometry Seminar

Title Systoles of convex energy hypersurfaces
Speaker, Affiliation Oliver Edtmair, ETH
Date, Time 23 September 2024, 15:15-16:30
Location HG G 19.1
Note special room!
Abstract Hofer-Wysocki-Zehnder proved that every strictly convex energy hypersurface in R^4 possesses a disk-like global surface of section. They asked whether a systole, i.e. a periodic orbit of least action, must span such a disk-like global surface of section. In my talk, I will give an affirmative answer to this question. Moreover, I will discuss some implications of this result concerning normalized symplectic capacities. This is based on joint work in progress with Abbondandolo and Kang.
Systoles of convex energy hypersurfacesread_more
HG G 19.1
Note special room!
* 30 September 2024
15:15-16:30 		Amanda Hirschi
Sorbonne University, Paris
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Symplectic Geometry Seminar

Title Open Gromov-Witten invariants in genus zero
Speaker, Affiliation Amanda Hirschi, Sorbonne University, Paris
Date, Time 30 September 2024, 15:15-16:30
Location HG G 19.1
Note special room!
Abstract In this talk, I will discuss work in progress, joint with Kai Hugtenburg, on defining open Gromov-Witten invariants (in genus zero) for embedded relatively spin Lagrangians in general closed symplectic manifolds. Our definition rests on the construction of a global Kuranishi chart for the relevant moduli spaces and is an invariant of the almost complex structure. We prove a relation between the invariants of Lagrangians related a Lagrangian cobordism. Time permitting, I will also discuss some results in higher genus.
Open Gromov-Witten invariants in genus zeroread_more
HG G 19.1
Note special room!
7 October 2024
15:15-16:30 		Remi Leclercq
Paris-Saclay University, Paris
Details

Symplectic Geometry Seminar

Title Local exactness of nearby Lagrangians and topological properties of orbits of Lagrangians
Speaker, Affiliation Remi Leclercq, Paris-Saclay University, Paris
Date, Time 7 October 2024, 15:15-16:30
Location HG G 43
Abstract The central point of this talk is to present a strategy for proving that Lagrangians which are displaceable by a Hamiltonian diffeomorphism admit a "Weinstein neighborhood of non-displacement", i.e. a neighborhood W of the given Lagrangian L such that if the image of L by a Hamiltonian diffeomorphism is included in W, it must intersect L. When the inclusion of L into M induces the 0-map at the level of first homology groups with real coefficients, this non-displacement property also holds for any Lagrangian included in W which is the image of L by a (non necessarily Hamiltonian) symplectomorphism. In both cases, non-displacement follows directly from "local exactness" of nearby Lagrangians, i.e. the fact that any Lagrangian in the Hamiltonian or symplectic orbit of L, included in W, is exact in W seen as a subset of T*L. I will give several natural examples for which such a neighborhood exists. I will then discuss applications of this line of ideas in terms of the topology of the Hamiltonian orbit of L, and in terms of C^0 symplectic geometry. This is joint work with Jean-Philippe Chassé.
Local exactness of nearby Lagrangians and topological properties of orbits of Lagrangiansread_more
HG G 43
14 October 2024
15:15-16:30 		Joé Brendel
Details

Symplectic Geometry Seminar

Title Product tori in S^2 x S^2 and Lagrangian packing
Speaker, Affiliation Joé Brendel,
Date, Time 14 October 2024, 15:15-16:30
Location HG G 43
Abstract A product torus in S^2 x S^2 is a Lagrangian torus obtained as the product of circles in the factors. The goal of this talk is to give a classification up to symplectomorphisms of such tori and illustrate that interesting things happen in case the symplectic form is non-monotone. Among other applications, we will answer a question about Lagrangian packings posed by Polterovich--Shelukhin. This is partially based on joint work with Joontae Kim.
Product tori in S^2 x S^2 and Lagrangian packingread_more
HG G 43
21 October 2024
15:15-16:30
Details

Symplectic Geometry Seminar

Title No seminar
Speaker, Affiliation
Date, Time 21 October 2024, 15:15-16:30
Location
No seminar
28 October 2024
15:15-16:30 		Adi Dickstein
Tel-Aviv University
Details

Symplectic Geometry Seminar

Title Symplectic topology and ideal-valued measures
Speaker, Affiliation Adi Dickstein, Tel-Aviv University
Date, Time 28 October 2024, 15:15-16:30
Location HG G 43
Abstract In various areas of mathematics there exist "big fiber theorems", these are theorems of the following type: "For any map in a certain class, there exists a 'big' fiber", where the class of maps and the notion of size changes from case to case. We will discuss three examples of such theorems, coming from combinatorics, topology and symplectic topology from a unified viewpoint provided by Gromov's notion of ideal-valued measures. We adapt the latter notion to the realm of symplectic topology, using an enhancement of Varolgunes’ relative symplectic cohomology to include cohomology of pairs. This allows us to prove symplectic analogues for the first two theorems, yielding new symplectic rigidity results. Necessary preliminaries will be explained. The talk is based on a joint work with Yaniv Ganor, Leonid Polterovich and Frol Zapolsky.
Symplectic topology and ideal-valued measures read_more
HG G 43
4 November 2024
15:15-16:30 		Robert Cardona
University of Barcelona
Details

Symplectic Geometry Seminar

Title Contact topology and time-dependent hydrodynamics
Speaker, Affiliation Robert Cardona, University of Barcelona
Date, Time 4 November 2024, 15:15-16:30
Location HG G 43
Abstract More than twenty years ago, Etnyre and Ghrist established a connection between Reeb fields and a class of stationary solutions to the 3D Euler equations for ideal fluids. In this talk, we present a new framework that allows assigning contact/symplectic invariants to large sets of time-dependent solutions to the Euler equations on any three-manifold with an arbitrary fixed Riemannian metric, thus broadening the scope of contact topological methods in hydrodynamics. We use it to prove a general non-mixing result for the infinite-dimensional dynamical system defined by the equation and to construct new conserved quantities obtained from embedded contact homology spectral invariants. This is joint work with Francisco Torres de Lizaur.
Contact topology and time-dependent hydrodynamicsread_more
HG G 43
11 November 2024
15:15-16:30
Details

Symplectic Geometry Seminar

Title No seminar
Speaker, Affiliation
Date, Time 11 November 2024, 15:15-16:30
Location
No seminar
18 November 2024
15:15-16:30 		Dylan Cant
Paris-Saclay University, Paris
Details

Symplectic Geometry Seminar

Title Spectral invariants and translated points
Speaker, Affiliation Dylan Cant, Paris-Saclay University, Paris
Date, Time 18 November 2024, 15:15-16:30
Location HG G 43
Abstract I will present recent work concerning a Floer theory persistence module associated to a Reeb flow and a contact isotopy \phi. The persistence module depends on a filling of the contact manifold. The spectrum of the persistence module is contained in the set of lengths of translated points of \phi relative the chosen Reeb flow. Under certain assumptions on the symplectic cohomology of the filling, the spectral invariants can be used to define a non-degenerate spectral norm on the contactomorphism group, and also spectral capacities for open sets. Various results, variations on the construction, and open questions concerning these structures will be discussed.
Spectral invariants and translated pointsread_more
HG G 43
25 November 2024
15:15-16:30 		Yuan Yao
Nantes Universite
Details

Symplectic Geometry Seminar

Title Anchored Symplectic Embeddings
Speaker, Affiliation Yuan Yao, Nantes Universite
Date, Time 25 November 2024, 15:15-16:30
Location HG G 43
Abstract Given two four-dimensional symplectic manifolds, together with knots in their boundaries, we define an ``anchored symplectic embedding'' to be a symplectic embedding, together with a two-dimensional symplectic cobordism between the knots (in the four-dimensional cobordism determined by the embedding). We use techniques from embedded contact homology to determine quantitative critera for when anchored symplectic embeddings exist, for many examples of toric domains. In particular we find examples where ordinarily symplectic embeddings exist, but they cannot be upgraded to anchored symplectic embeddings unless one enlarges the target domain.
Anchored Symplectic Embeddingsread_more
HG G 43
* 2 December 2024
09:00-10:00 		Prof. Dr. Yaron Ostrover
Details

Symplectic Geometry Seminar

Title Viterbo's Conjecture: Early Developments
Speaker, Affiliation Prof. Dr. Yaron Ostrover,
Date, Time 2 December 2024, 09:00-10:00
Location HG G 19.2
Zoom Call
Abstract In this series of talks, I will provide an overview of Viterbo's volume-capacity conjecture, a symplectic isoperimetric-type inequality concerning symplectic capacities of convex domains in the classical phase space. Specifically, in the first talk, we will explore Viterbo's conjecture from the perspective of asymptotic geometric analysis. The second talk will focus on Minkowski billiard dynamics, and the characteristic foliation on convex polytopes. Finally, in the third talk, we will present a counterexample to Viterbo's conjecture and discuss potential future research directions. These talks are based on joint work with S. Artstein-Avidan, P. Haim-Kislev, E. Gluskin, R. Karasev, and V. Milman. Zoom: https://ethz.zoom.us/j/64239710101
Viterbo's Conjecture: Early Developmentsread_more
HG G 19.2
Zoom Call
* 3 December 2024
10:30-12:00 		Prof. Dr. Yaron Ostrover
Details

Symplectic Geometry Seminar

Title Viterbo's Conjecture and Minkowski Billiards
Speaker, Affiliation Prof. Dr. Yaron Ostrover,
Date, Time 3 December 2024, 10:30-12:00
Location HG G 19.1
Zoom Call
Abstract In this series of talks, I will provide an overview of Viterbo's volume-capacity conjecture, a symplectic isoperimetric-type inequality concerning symplectic capacities of convex domains in the classical phase space. Specifically, in the first talk, we will explore Viterbo's conjecture from the perspective of asymptotic geometric analysis. The second talk will focus on Minkowski billiard dynamics, and the characteristic foliation on convex polytopes. Finally, in the third talk, we will present a counterexample to Viterbo's conjecture and discuss potential future research directions. These talks are based on joint work with S. Artstein-Avidan, P. Haim-Kislev, E. Gluskin, R. Karasev, and V. Milman. Zoom: https://ethz.zoom.us/j/65744003648
Viterbo's Conjecture and Minkowski Billiardsread_more
HG G 19.1
Zoom Call
* 4 December 2024
13:00-14:30 		Prof. Dr. Yaron Ostrover
Details

Symplectic Geometry Seminar

Title Viterbo's Conjecture: Recent Progress and Future Directions
Speaker, Affiliation Prof. Dr. Yaron Ostrover,
Date, Time 4 December 2024, 13:00-14:30
Location HG G 19.1
Zoom Call
Abstract In this series of talks, I will provide an overview of Viterbo's volume-capacity conjecture, a symplectic isoperimetric-type inequality concerning symplectic capacities of convex domains in the classical phase space. Specifically, in the first talk, we will explore Viterbo's conjecture from the perspective of asymptotic geometric analysis. The second talk will focus on Minkowski billiard dynamics, and the characteristic foliation on convex polytopes. Finally, in the third talk, we will present a counterexample to Viterbo's conjecture and discuss potential future research directions. These talks are based on joint work with S. Artstein-Avidan, P. Haim-Kislev, E. Gluskin, R. Karasev, and V. Milman. Zoom: https://ethz.zoom.us/j/68488661786
Viterbo's Conjecture: Recent Progress and Future Directionsread_more
HG G 19.1
Zoom Call
9 December 2024
15:15-16:15 		Matthias Meiwes
Tel Aviv University
Details

Symplectic Geometry Seminar

Title Entropy and links in 3D Reeb flows
Speaker, Affiliation Matthias Meiwes, Tel Aviv University
Date, Time 9 December 2024, 15:15-16:15
Location HG G 43
Abstract An important quantity for the orbit complexity of a dynamical system is its topological entropy. Recently, several fruitful approaches were found to express topological entropy of Hamiltonian or Reeb dynamics in terms of Floer theory or contact homology. For a 3D Reeb flow and a link of periodic orbits, Alves and Pirnapasov introduced the notion of the homotopical growth rate in the link complement, defined by counting certain "essential" homotopy classes of periodic orbits in the complement of that link. In my talk, I will explain how topological entropy of a Reeb flow can be recovered through homotopical growth rates in complements of links of periodic orbits, given some mild assumptions on the flow. I will moreover explain some applications of this result and discuss stability features of the topological entropy of Reeb flows. Partly based on joint work with M. Alves, L. Dahinden, and A. Pirnapasov.
Entropy and links in 3D Reeb flowsread_more
HG G 43
16 December 2024
15:15-16:15 		Tom Mrowka
MIT
Details

Symplectic Geometry Seminar

Title Instanton Floer homology for 3-manifolds, knot and webs: what’s next?
Speaker, Affiliation Tom Mrowka, MIT
Date, Time 16 December 2024, 15:15-16:15
Location HG G 43
Abstract Floer homology in its Monopole, Heegard and ECH version’s has proved a powerful tool for the study of the geometry and topology of three manifolds. Their older cousin instanton Floer homology also has its share of trophies but remains more mysterious and harder to compute. This talk will survey a few highlights of applications of the theory and problems that remain to be solved and prospects for the future.
Instanton Floer homology for 3-manifolds, knot and webs: what’s next?read_more
HG G 43
23 December 2024
15:15-16:15
Details

Symplectic Geometry Seminar

Title No seminar
Speaker, Affiliation
Date, Time 23 December 2024, 15:15-16:15
Location HG G 43
No seminar
HG G 43

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