Geometry & Dynamics Seminar 2024-25

Some seminar talks will take place in Schreiber Building, room 309, and in addition 

will be broadcasted via the zoom app, while other talks will run entirely via the zoom app.

The seminar will take place on Wednesdays at 14:10.

Please check each announcement since this is sometimes changed. 

The zoom link is available upon request by email.

 

06.11.2024, 14:10 (Wednesday)	Orientation meeting for students
Location:	Schreiber bldg., room 309, Tel-Aviv University
13.11.2024, 14:10 (Wednesday)	Dylan Cant (Université Paris-Saclay)
Title:	Spectral invariants and eternal classes in symplectic cohomology
Location:	Zoom session and screening in Schreiber 309
Abstract:	I will discuss special classes in the symplectic cohomology of a semipositive and convex-at-infinity symplectic manifold $W$. The classes under consideration lie in the image of every continuation map (for this reason, we call them eternal classes as they are never born and never die). Non-eternal classes in symplectic cohomology can be used to define spectral invariants for contact isotopies of the ideal boundary $Y$. These spectral invariants of non-eternal classes behave sub-additively with respect to the pair-of-pants product. When the unit element in SH is non-eternal, we define two spectral pseudo-metrics on the universal cover of the group of contactomorphisms. The first is a spectral version of the Shelukhin-Hofer oscillation norm, and the second is an analog the Shelukhin-Hofer L1 norm. The spectral pseudo-metrics are non-negative, satisfy the triangle inequality, and bound the Shelukhin-Hofer norms from below. The spectral invariants also lead to a spectral capacity for open sets, similar to the measurements introduced by Sandon.
20.11.2024, 14:10 (Wednesday)	Shira Tanny (Weizmann Institute of Science)
Title:	From Gromov–Witten theory to the closing lemma
Location:	Schreiber 309 and zoom session
Abstract:	An old question of Poincaré concerns creating periodic orbits via perturbations of a flow/diffeomorphism. While pseudoholomorphic methods have successfully addressed this question in dimensions 2-3, the higher-dimensional case remains less understood. I will describe a connection between this question and Gromov–Witten invariants, which goes through a new class of invariants of symplectic cobordisms. This is a joint work with Julian Chaidez.
27.11.2024, 14:10 (Wednesday)	Andrew Lobb (Durham University)
Title:	Symplectic topology and peg problems
Location:	Zoom session
Abstract:	The Square Peg Problem (SPP), formulated by Toeplitz in 1911 and still unsolved, asks whether every Jordan curve contains four points at the vertices of a square. We shall discuss how, when the Jordan curve is smooth, SPP and related peg problems can be interpreted as questions in symplectic topology, and deduce some consequences both for smooth curves and for other classes.   Joint work with Josh Greene.
04.12.2024, 14:10 (Wednesday)	Peter Albers (Heidelberg University)
Title:	Outer symplectic billiard
Location:	Zoom session and screening in Schreiber 309
Abstract:	We will discuss outer symplectic billiard which is a billiard-type correspondence defined by some fixed submanifold in a symplectic vector space. Particularly interesting cases are that the submanifold is a curve, Lagrangian or a hypersurface. All of these can be thought of possible generalization of outer billiards in the plane. The theory is particularly nice for symplectically convex curves but existence theory for periodic orbits is a somewhat counterintuitive. In the Lagrangian case we will make a curious use of a Theorem by H. Hopf on bilinear, symmetric without zero-divisors. This is joint work with Ana Chavez Caliz and Sergei Tabachnikov.
11.12.2024, 14:10 (Wednesday)	Marcelo Atallah (University of Sheffield)
Title:	The number of periodic points of surface symplectomorphisms
Location:	Zoom session and screening in Schreiber 309
Abstract:	A celebrated result of Franks shows that a Hamiltonian diffeomorphism of the sphere with more than two fixed points must have infinitely many periodic points. We present a symplectic proof of a variant of this phenomenon for symplectomorphisms of surfaces of higher genus that are isotopic to the identity; it implies an upper bound for the Floer-homological count of the number of fixed points of a symplectomorphism with finitely many periodic points. From a higher dimensional viewpoint, this can be understood as evidence for a non-Hamiltonian variant of Shelukhin’s result on the Hofer-Zehnder conjecture. Furthermore, we discuss the construction of a symplectic flow on a surface of any positive genus having a single fixed point and no other periodic orbits. This is joint work with Marta Batoréo and Brayan Ferreira.
18.12.2024, 14:10 (Wednesday)	Stefan Nemirovski (Steklov Mathematical Institute and Ruhr University Bochum)
Title:	Unknotting Lagrangian $S^1\times S^{n-1}$ in $\mathbb{R}^{2n}$
Location:	Zoom session and screening in Schreiber 309
Abstract:	The purpose of the talk is to describe the classification of Lagrangian embeddings of $S^1\times S^{n-1}$ in the standard symplectic space $\mathbb{R}^{2n}$ up to smooth isotopy for all $n\ge 3$.
25.12.2024, 14:10 (Wednesday)	Jake Solomon (Hebrew University of Jerusalem)
Title:	Toward open mirror symmetry for Fano manifolds
Location:	Schreiber 309 and zoom session
Abstract:	Genus zero open Gromov-Witten invariants of a Lagrangian L in a symplectic manifold X count J-holomorphic disks in X with boundary in L along with correction terms. For certain L, these counts recover Welschinger's real enumerative invariants. When X is a Fano manifold, mirror symmetry predicts that L should correspond to an algebraic object called a matrix factorization. I will explain how to define numerical invariants of matrix factorizations equipped with the additional structure of a non-Archimedean norm. The norm carries the information of the action filtration on the Lagrangian Floer complex. Evidence will be presented that the numerical invariants of matrix factorizations recover open Gromov-Witten invariants. No prior background in mirror symmetry or matrix factorizations will be assumed. This is joint work with May Sela.
01.01.2025, 14:10 (Wednesday)	Snir Ben Ovadia (Pennsylvania State University)
Title:	Exponential volume limits
Location:	Schreiber 309 and zoom session
Abstract:	We prove that when the pushed volume of a closed manifold converges exponentially fast to a measure, then the limiting measure is an SRB measure.
08.01.2025, 14:10 (Wednesday)	Marcelo R.R. Alves (University of Antwerp)
Title:	From curve shortening to Birkhoff sections of geodesic flows
Location:	Zoom session and screening in Schreiber 309
Abstract:	In this talk, based on joint work with Marco Mazzucchelli, I will present some new results on the dynamics of geodesic flows of closed Riemannian surfaces, proved using the curve shortening flow. The first result is a forced existence theorem for orientable closed Riemannian surfaces of positive genus, asserting that the existence of a contractible simple closed geodesic \gamma forces the existence of infinitely many closed geodesics in every primitive free homotopy class of loops and intersecting \gamma. I will then explain how this type of result can be used to show the existence of Birkhoff sections for the geodesic flow of any closed orientable Riemannian surface.
15.01.2025, 14:10 (Wednesday)	Yaniv Ganor (Holon Institute of Technology)
Title:	Persistence in Wrapped Floer Homology and Poisson Bracket Invariants
Location:	Schreiber 309 and zoom session
Abstract:	The Poisson bracket invariants, introduced by Buhovsky, Entov and Polterovich, are invariants of quadruples of closed sets in symplectic manifolds. Their nonvanishing has implications to the existence of Hamlitonian trajectories between pairs of the sets in the quadruple, with bound on the time-length. In this talk, we will describe a work in progress, where we obtain lower bounds of the Poisson bracket invariants of certain configurations arising in the completion of Liouville manifolds, in terms of the barcode of wrapped Floer homology. This work is inspired by Entov and Polterovich, who proved similar results for Lagrangian cobordisms between two contact manifolds, using persistence in Legendrian contact homology. Our main examples are cotangent bundles of Riemannian manifolds, where the quadruple comprises two cosphere bundles of different radii, and two cotangent fibers above different points. In this example the nonvanishing of the Poisson bracket invariant implies the existence of Hamiltonian trajectories going between the fibers, with an explicit bound on their time-length, for certain Hamiltonian perturbations of the geodesic flow.
22.01.2025, 14:10 (Wednesday)	Emmanuel Opshtein (University of Strasbourg)
Title:	Symplectic/contact rigidity of some Lagrangian/Legendrian skeleta in dimension 4
Location:	Zoom session and screening in Schreiber 309
Abstract:	In the simplest framework of a symplectic manifold with rational symplectic class, a symplectic polarization is a smooth symplectic hypersurface Poincaré-Dual to a multiple of the symplectic class. Their complement retract to some skeleta, which are quite often isotropic CW-complexes. These notions were introduced by Biran and he exhibited symplectic rigidity properties of these skeleta. In later work, I generalized the notion of symplectic polarizations to any closed symplectic manifold with a view towards effective constructions of symplectic embeddings. In the present talk, I will explain how this notion of polarization can be generalized further to the affine setting in dimension 4 and how it leads to new interesting results on the side of the symplectic rigidity of Lagrangian skeleta. Using an argument « à la Mohnke », I will present an analogue of these rigidities in contact geometry, that seems very new to us. The talk will focus on examples. Joint work with Felix Schlenk.
29.01.2025, 14:10 (Wednesday)	Michael Entov (Technion)
Title:	New geometric measurements of Legendrian isotopies
Location:	Schreiber 309 and zoom session
Abstract:	Relative Symplectic Field Theory associates to a (non-degenerate) pair formed by a Legendrian submanifold and a contact form on a contact manifold a version of the Legendrian contact homology, and to an exact Lagrangian cobordism between Legendrian submanifolds a morphism between the corresponding Legendrian contact homologies. The Legendrian contact homology comes equipped with the action filtration, induced by the actions of the Reeb chords, and thus gives rise to persistence modules. The exact Lagrangian cobordisms then induce morphisms between the persistence modules. I will discuss the information on various new geometric measurements of Legendrian isotopies, and, in particular, of positive Legendrian isotopies, provided by the machinery above and by the theory of persistence modules. This is a work in progress, joint with L.Polterovich.
19.03.2025, 14:10 (Wednesday)	Daniel Tsodikovich (ISTA)
Title:	Local rigidity of integrable symplectic billiards
Location:	Schreiber 309 and zoom session
Abstract:	Symplectic billiards were introduced by Albers and Tabachnikov as an alternative billiard model where the generating function is the area form. The resulting system behaves somewhat differently from the usual billiards, but as it turns out, several rigidity results for billiards have been recently adapted to this setting. In this talk, we explain that the integrability of ellipses is locally rigid: an integrable domain near an ellipse is an ellipse. This is an adaptation of the result of Avila, De Simoi, and Kaloshin, for Birkhoff billiards.
26.03.2025, 16:10 (Wednesday)	Vukašin Stojisavljević (University of Montreal)
Title:	On certain C^0-aspects of contactomorphism groups
Location:	Zoom session
Abstract:	We will explore certain C^0-rigidity and flexibility phenomena in the study of contact transformations. In particular, we will show how the dichotomy between contact squeezing and non-squeezing is related to the Rokhlin property of the group of contact homeomorphisms. We will also define a new conjugation-invariant norm on the group of smooth contactomorphisms and study its relation to the contact fragmentation norm. The main technical ingredient is a result stating that Sandon's spectral norm is C^0-locally bounded. The talk is based on a joint work with Baptiste Serraille.
02.04.2025, 14:10 (Wednesday)	Isabelle Charton (Tel Aviv University)
Title:	Monotone Symplectic Manifolds with a Torus Action of Complexity One
Location:	Schreiber bldg., room 309, Tel Aviv University (and online via zoom).
Abstract:	A compact symplectic manifold $(M, \omega)$ is called positive monotone if its first Chern class is a positive multiple of $[\omega]$ in the second de Rham group $H^2(M)$. A Fano variety is a smooth complex variety that admits a holomorphic embedding into $\mathbb{C} P^N$ for some $N$. Such a variety can be endowed with a symplectic form such that it becomes a positive monotone symplectic manifold. For this reason, positive monotone symplectic manifolds are considered the symplectic counterparts of smooth Fano varieties. In the field of symplectic geometry, a general outstanding issue is understanding in what context positive monotone symplectic manifolds differ from Fano varieties. In low dimensions, namely two and four, it has been proven by Gromov, Taubes, McDuff, and Ohat-Ono that any positive monotone symplectic manifold is symplectomorphic to a Fano variety. Starting from dimension twelve, work by Fine and Panov provides examples of positive monotone symplectic manifolds that are not even homotopy equivalent to a Fano variety. In this talk, I will explain what is known about the differences between Fano varieties and positive monotone symplectic manifolds endowed with a Hamiltonian action of a compact torus $T$. In particular, I will present new results for the case where the complexity of the action is one, i.e., $\frac{1}{2}\operatorname{dim}(M)-\operatorname{dim}(T)=1$. This talk is based on joint work with Liat Kessler, Silvia Sabatini, and Daniele Sepe.
23.04.2025, 14:10 (Wednesday)	Oliver Edtmair (ETH Zürich)
Title:	Volume filling ellipsoids
Location:	Zoom session and screening in Schreiber 309
Abstract:	I will explain how to fill the full volume of any compact connected symplectic 4-manifold with smooth boundary with a single symplectic ellipsoid. This can be seen as a strong version of Biran’s famous packing stability theorem and has interesting consequences concerning the subleading asymptotics of various symplectic Weyl laws. The embedding construction relies on a quantitative refinement of Banyaga’s classical theorem on the simplicity and perfectness of Hamiltonian diffeomorphism groups, which I will also explain. Recently, Cristofaro-Gardiner and Hind constructed symplectic domains (with non-regular boundary) for which packing stability breaks down. I will explain some progress towards pinpointing the exact transition point between packing stability and failure thereof and mention open questions and conjectures.
07.05.2025, 14:10 (Wednesday)	Rei Henigman (Tel Aviv University)
Title:	Classification of symplectic non-Hamiltonian circle actions on 4-manifolds
Location:	Schreiber bldg., room 309, Tel Aviv University (and online via zoom).
Abstract:	Famously, Karshon gave a full classification of Hamiltonian circle actions on compact connected symplectic 4-manifolds up to equivariant symplectomorphism, by combinatorial invariants. In this talk, I will describe how to extend her result to non-Hamiltonian symplectic circle actions, defining new invariants for non-Hamiltonian actions by using McDuff's circle-valued Hamiltonians. These new invariants capture non-trivial topological properties of the spaces, in contrast to the combinatorial nature of the invariants in the Hamiltonian case.
14.05.2025, 14:10 (Wednesday)	Erman Çineli (ETH Zürich)
Title:	Closed orbits of dynamically convex Reeb flows
Location:	Zoom session (and screening in Schreiber bldg., room 309, Tel Aviv University).
Abstract:	In this talk we will discuss two results on the multiplicity problem for prime closed orbits of dynamically convex Reeb flows on the boundary of a star-shaped domain in $\mathbb{R}^{2n}$. The first result asserts that such a flow has at least n prime closed Reeb orbits, improving the previously known lower bound by a factor of two. The second main theorem is that when, in addition, the domain is centrally symmetric and the Reeb flow is non-degenerate, the flow has either exactly n or infinitely many prime closed orbits. This is a joint work with Basak Gurel and Viktor Ginzburg.
21.05.2025, 14:10 (Wednesday)	Stefan Matijević (Ruhr University Bochum)
Title:	Systolic S^1-index and characterization of non-smooth Zoll convex bodies
Location:	Zoom session (and screening in Schreiber bldg., room 309, Tel Aviv University).
Abstract:	We define the systolic S^1-index of a convex body as the Fadell–Rabinowitz index of the space of centralized generalized systoles associated with its boundary. We show that this index is a symplectic invariant. Using the systolic S^1-index, we propose a definition of generalized Zoll convex bodies and prove that this definition is equivalent to the usual one in the smooth setting. Moreover, we show how generalized Zoll convex bodies can be characterized in terms of their Gutt–Hutchings capacities and we prove that the space of generalized Zoll convex bodies is closed in the space of all convex bodies. As a corollary, we establish that if the interior of a convex body is symplectomorphic to the interior of a ball, then such a convex body must be generalized Zoll, and in particular Zoll if its boundary is smooth. Finally, we discuss some examples.
28.05.2025, 14:10 (Wednesday)	Yoel Groman (Hebrew University of Jerusalem)
Title:	Almost toric fibrations on K3 surfaces
Location:	Schreiber bldg., room 309, Tel Aviv University (and online via zoom).
Abstract:	It is a long standing conjecture that a toric degeneration of Calabi-Yau manifolds gives rise to a Lagrangian torus fibration on the general fiber, whose base is the intersection complex with a certain integral affine structure defined away from a codimension 2 set. I will discuss this in the case of K3 surfaces. Joint with Pranav Chakravarthy. https://arxiv.org/abs/2502.04304
04.06.2025, 14:10 (Wednesday)	Umberto Hryniewicz (RWTH Aachen University)
Title:	Perturbing critical points away in dimensions two and three
Location:	Zoom session (and screening in Schreiber bldg., room 309, Tel Aviv University).
Abstract:	This is an ongoing joint project with Lima, de Rezende and Silveira. We propose to study the very simple but fundamental question regarding bifurcation theory of critical points: When can an isolated critical point of a smooth function be destroyed by a C^2-small perturbation of the function? Of course, non-vanishing of local Morse homology is an obstruction, and we study whether it is the only obstruction. I will explain why in dimensions two and three local Morse homology is expected to be the only obstruction, and why in dimension four the situation is absolutely unclear.
11.06.2025, 14:10 (Wednesday)	Joe Brendel (ETH Zürich)
Title:	TBA
Location:	Zoom session (and screening in Schreiber bldg., room 309, Tel Aviv University).
Abstract:	TBA
18.06.2025, 14:10 (Wednesday)	Michael Brandenbursky (BGU)
Title:	TBA
Location:	Schreiber bldg., room 309, Tel Aviv University (and online via zoom).
Abstract:	TBA
25.06.2025, 14:10 (Wednesday)	Marina Ville (University of Tours)
Title:	TBA
Location:	Schreiber bldg., room 309, Tel Aviv University (and online via zoom).
Abstract:	TBA
02.07.2025, 14:10 (Wednesday)	Adi Dickstein (Tel Aviv University)
Title:	TBA
Location:	Schreiber bldg., room 309, Tel Aviv University (and online via zoom).
Abstract:	TBA
02.07.2025, 16:10 (Wednesday)	Jakob Hedicke (University of Montreal)
(PLEASE NOTE CHANGE IN TIME!)
Title:	TBA
Location:	Zoom session
Abstract:	TBA