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Autumn Semester 2022

Date / Time Speaker Title Location
26 September 2022
15:15-16:30 		Yusuke Kawamoto
ETH Zürich
Event Details

Symplectic Geometry Seminar

Title Donaldson divisors and Entov-Polterovich quasimorphisms
Speaker, Affiliation Yusuke Kawamoto, ETH Zürich
Date, Time 26 September 2022, 15:15-16:30
Location HG G 43
Abstract We discuss a question of Borman from 2012 on the relation between Entov-Polterovich quasimorphisms on a symplectic manifold and a Donaldson divisor therein.
Donaldson divisors and Entov-Polterovich quasimorphismsread_more
HG G 43
3 October 2022
15:15-16:30 		Joé Brendel
Université de Neuchâtel
Event Details

Symplectic Geometry Seminar

Title Local exotic tori
Speaker, Affiliation Joé Brendel, Université de Neuchâtel
Date, Time 3 October 2022, 15:15-16:30
Location HG G 43
Abstract We discuss exotic Lagrangian tori in dimension greater than or equal to six. First, we give another approach to Auroux's result that there are infinitely many tori in $\mathbb{R}^6$ which are distinct up to symplectomorphisms of the ambient space. The exotic tori we construct naturally appear in a two-parameter family, some of which are not monotone. Second, we show that our construction can be carried out purely locally in a Darboux chart and that (provided the ambient symplectic manifold is tame) the resulting tori are also distinct up to symplectomorphisms.
Local exotic toriread_more
HG G 43
10 October 2022
15:15-16:30 		Nicolas Berkouk
EPF Lausanne
Event Details

Symplectic Geometry Seminar

Title On the non-stability of the sheaf-function correspondence, with application towards persistent K-theory
Speaker, Affiliation Nicolas Berkouk, EPF Lausanne
Date, Time 10 October 2022, 15:15-16:30
Location HG G 43
Abstract The sheaf-function correspondence identifies the group of constructible functions on a real analytic manifold M with the Grothendieck group of constructible sheaves on M . When M is a finite dimensional real vector space, Kashiwara-Schapira have recently introduced the convolution distance between sheaves of k-vector spaces on M . In this talk, we will characterize distances on the group of constructible functions on a real finite dimensional vector space that can be controlled by the convolution distance through the sheaf-function correspondence. Our main result asserts that such distances are almost trivial: they vanish as soon as two constructible functions have the same Euler integral. Finally, we will give consequences of our result for the stability of the K-theory of persistence modules.
On the non-stability of the sheaf-function correspondence, with application towards persistent K-theoryread_more
HG G 43
17 October 2022
15:15-16:30 		Paul Biran
ETH Zürich
Event Details

Symplectic Geometry Seminar

Title Filtered Fukaya Categories - teaser trailer
Speaker, Affiliation Paul Biran, ETH Zürich
Date, Time 17 October 2022, 15:15-16:30
Location HG G 43
Abstract Why is it not straightforward to get Fukaya categories to be filtered? And why do we care about this? This will be a introductory talk, in which we will try to answer the questions above, and outline some partials solutions. Our talk will serve as a warm up for the talk planned on 24.10 by Gionvanni Ambrosioni which will present a more general approach to these questions.
Filtered Fukaya Categories - teaser trailerread_more
HG G 43
24 October 2022
15:15-16:30 		Giovanni Ambrosioni
ETH Zürich
Event Details

Symplectic Geometry Seminar

Title Filtered Fukaya Categories
Speaker, Affiliation Giovanni Ambrosioni, ETH Zürich
Date, Time 24 October 2022, 15:15-16:30
Location HG G 43
Abstract It is known that Fukaya categories are not filtered $A_\infty$ categories for arbitrary choices of the parameters needed for their construction, but only weakly-filtered. In this talk we will present a trick to construct classes of such parameters so that the associated Fukaya categories are filtered. Then, we will discuss how different choices of parameters will affect the persistence structure of Fukaya categories at the derived level. If time permits we will show some applications of the filtered structures on Fukaya categories.
Filtered Fukaya Categoriesread_more
HG G 43
31 October 2022
15:15-16:30 		Patricia Dietzsch
ETH Zürich
Event Details

Symplectic Geometry Seminar

Title Dehn twists along real Lagrangian spheres
Speaker, Affiliation Patricia Dietzsch, ETH Zürich
Date, Time 31 October 2022, 15:15-16:30
Location HG G 43
Abstract A major tool in the study of the Dehn twist along a Lagrangian sphere is Seidel'slong exact sequence. This sequence comes with a distinguished element A in the Floer homology group of the Dehn twist. In this talk we will discuss a property of A in case the Dehn twist is a monodromy in a real Lefschetz fibration. We will see that the real structure induces an automorphism on the Floer homology group of the Dehn twist and that A is a fixed point.
Dehn twists along real Lagrangian spheresread_more
HG G 43
7 November 2022
15:15-16:30 		Alessio Pellegrini
ETH Zürich
Event Details

Symplectic Geometry Seminar

Title A Bangert-Hingston Theorem for Starshaped Hypersurfaces
Speaker, Affiliation Alessio Pellegrini, ETH Zürich
Date, Time 7 November 2022, 15:15-16:30
Location HG G 43
Abstract In the first part of the talk we will discuss some aspects of a celebrated theorem due to Bangert and Hingston which says the following: on any closed manifold Q, which is not a circle and has fundamental group Z, there exist prime-many geometrically distinct closed geodesics. In the second part we will explain how Bangert and Hingston's theorem can be restated in terms of Hamiltonian dynamics on S*Q and discuss the natural generalization from geodesics to Reeb orbits. Under an additional circle action assumption and the use of Floer theory, we proceed to give a proof of a Bangert and Hingston type result for closed Reeb orbits on non-degenerate starshaped hypersurfaces inside T*Q.
A Bangert-Hingston Theorem for Starshaped Hypersurfacesread_more
HG G 43
14 November 2022
15:15-16:30 		Adrian Dawid
ETH Zürich
Event Details

Symplectic Geometry Seminar

Title Topological Entropy and Persistent Floer Homology
Speaker, Affiliation Adrian Dawid, ETH Zürich
Date, Time 14 November 2022, 15:15-16:30
Location HG G 43
Abstract A recent result of Cineli, Ginzburg and Gürel establishes a connection between the topological entropy of a Hamiltonian diffeomorphism and the persistence features of Lagrangian Floer homology. Following Cineli-Ginzburg-Gürel, we will explain the notion of barcode entropy that measures the exponential growth of not-too-short bars in a sequence of barcodes. Specifically, we will examine the barcodes of Lagrangian Floer homology for a pair of weakly exact Hamiltonian isotopic Lagrangian submanifolds in a closed symplectic manifold. By applying iterations of a Hamiltonian diffeomorphism we obtain a sequence of barcodes. We explain a result of Cineli-Ginzburg-Gürel asserting that the barcode entropy of this sequence is bounded above by the topological entropy of the Hamiltonian diffeomorphism. Lastly, we give some reasons why a reverse inequality is not possible in this simple setting.
Topological Entropy and Persistent Floer Homologyread_more
HG G 43
28 November 2022
15:15-16:30 		Jean-Philippe Chassé
ETH Zürich
Event Details

Symplectic Geometry Seminar

Title Sequences of Lagrangian submanifolds respecting uniform Riemannian bounds and their limits in various metrics
Speaker, Affiliation Jean-Philippe Chassé, ETH Zürich
Date, Time 28 November 2022, 15:15-16:30
Location HG G 43
Abstract Recent years have seen the appearance of a plethora of symplectically-meaningful metrics on collections of Lagrangian submanifolds. Indeed, on top of the better-known Lagrangian Hofer metric and the spectral metric, Biran, Cornea, and Shelukhin have for example introduced the so-called shadow metrics on these spaces. These new metrics are particularly interesting, as they allow to compare Lagrangian submanifolds which may not even have the same homotopy type. It is however unclear what it means for two Lagrangian submanifolds to be nearby in these metrics. I will explain how—under the presence of bounds coming from Riemannian geometry—being close can be understood in terms of the classical Hausdorff metric, giving thus a much better understanding of the situation.
Sequences of Lagrangian submanifolds respecting uniform Riemannian bounds and their limits in various metricsread_more
HG G 43
5 December 2022
15:15-16:30 		Oliver Edtmair
U.C. Berkeley
Event Details

Symplectic Geometry Seminar

Title Symplectic Weyl laws – an elementary perspective
Speaker, Affiliation Oliver Edtmair, U.C. Berkeley
Date, Time 5 December 2022, 15:15-16:30
Location HG G 43
Abstract Spectral invariants defined via Embedded Contact Homology (ECH)or the closely related Periodic Floer Homology (PFH) satisfy a Weyl law: Asymptotically, they recover symplectic volume. This Weyl law has led to striking applications in dynamics and C^0 symplectic geometry. For example, it plays a key role in the proof of the smooth closing lemma for three-dimensional Reeb flows and area preserving surface diffeomorphisms, and in the proof of the simplicity conjecture. ECH and PFH are highly sophisticated theories whose construction in particular relies on Seiberg-Witten theory. I will explain how one can use much more elementary methods (no Floer or Gauge theory) to define spectral invariants satisfying an analogous Weyl law with similar applications. I hope that this elementary perspective makes the underlying mechanisms of the symplectic Weyl law more transparent. This is based on joint work with Michael Hutchings.
Symplectic Weyl laws – an elementary perspectiveread_more
HG G 43
12 December 2022
15:15-16:30 		Alex Oancea
Université de Strasbourg
Event Details

Symplectic Geometry Seminar

Title The secondary continuation map in Floer theory
Speaker, Affiliation Alex Oancea, Université de Strasbourg
Date, Time 12 December 2022, 15:15-16:30
Location HG G 43
Abstract I will discuss the following new phenomenon in Floer theory: in situations where continuation maps are not homotopy equivalences, so-called secondary continuation maps defined by interpolation carry nontrivial topological information. In a first example, which deals with Rabinowitz Floer homology, the secondary continuation map realizes the Poincaré duality isomorphism and intertwines graded Frobenius algebra structures. In a second example, motivated by string topology, the secondary continuation map controls extensions of the loop coproduct which, together with the loop product, fit into the structure of a unital infinitesimal bialgebra. The talk will be based on joint work with Kai Cieliebak and Nancy Hingston.
The secondary continuation map in Floer theoryread_more
HG G 43

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