Geometry & Dynamics Seminar 2021-22


The virtual seminar will run via the zoom application, on Wednesdays at 14:10.

Please check each announcement since this is sometimes changed.

 

Upcoming Talks        Previous Talks        Previous Years










20.10.2021, 14:10 (Wednesday) Patrick Iglesias-Zemmour (CNRS, HUJI)



Title: Every symplectic manifold is a (linear) coadjoint orbit
Location: Zoom session, the link is available upon request by email



Abstract: I will show how every symplectic manifold (Hausdorff and second countable)
is a coadjoint orbit of the group of automorphisms of its integration
bundle, for the linear coadjoint action, even when the symplectic form
is not integral, i.e., when the group of periods is dense in the real
line. In this case the integration bundle is not a manifold because
its torus of period is not a circle but an "irrational torus". This
theorem answers a question asked by a few students, in particular on
MathOverFlow: Is there a universal model for symplectic manifolds? The
answer is "yes".  They are all coadjoint orbits.








27.10.2021, 14:10 (Wednesday)
Daniel Tsodikovich (Tel Aviv University)




Title:
Billiard Tables with rotational symmetry
Location: Zoom session, the link is available upon request by email



Abstract: Consider the following simple geometric fact: the only centrally symmetric
convex curve of constant width is a circle. The condition of having constant
width is equivalent for the (Birkhoff) billiard map to have a 1-parameter
family of two periodic orbits. We generalize this statement to curves that
are invariant under a rotation by angle \frac{2\pi}{k},  for which the
billiard map has a 1-parameter family of k-periodic orbits. We will also
consider a similar setting for other billiard systems: outer billiards,
symplectic billiards, and (a special case of) Minkowski billiards.
Joint work with Misha Bialy.









03.11.2021, 16:10 (Wednesday) Egor Shelukhin (University of Montreal)
(PLEASE NOTE CHANGE IN TIME!)




Title: Hamiltonian no-torsion
Location: Zoom session, the link is available upon request by email



Abstract: We generalize in several ways Polterovich's well-known theorem that the
Hamiltonian group of a closed symplectically aspherical manifold admits
no non-trivial elements of finite order. We prove an analogous statement
for Calabi-Yau and negatively monotone manifolds. For positively monotone
manifolds we prove that non-trivial torsion implies geometric uniruledness
of the manifold, answering a question of McDuff-Salamon. Moreover, in this
case the following symplectic Newman theorem holds: a small Hofer-ball
around the identity contains no finite subgroup. This is joint work with
Marcelo Atallah.








10.11.2021, 14:10 (Wednesday)
Umut Varolgunes (Stanford University, University of Edinburgh)




Title: Trying to quantify Gromov's non-squeezing theorem
Location: Zoom session, the link is available upon request by email



Abstract: Gromov's celebrated result says (colloquially) that one cannot symplectically
embed a ball of radius 1.1 into a cylinder of radius 1. I will show that in
4d if one removes from this ball a Lagrangian plane passing through the
origin, then such an embedding becomes possible. I will also show that this
gives the smallest Minkowski dimension of a closed subset with this property.
I will end with many questions. This is based on joint work with K. Sackel,
A. Song and J. Zhu.








17.11.2021, 14:10 (Wednesday) Pazit Haim Kislev (Tel Aviv University)



Title: Symplectic capacities of p-products
Location: Zoom session, the link is available upon request by email



Abstract: In this talk we discuss symplectic capacities of convex domains and their
behavior with respect to symplectic p-products. One application, by using
a "tensor power trick", is to show that it is enough to prove Viterbo's
volume-capacity conjecture in the asymptotic regime when the dimension is
sent to infinity. In addition, we introduce a conjecture about higher order
capacities of p-products and show that if it holds then there are no
non-trivial p-decompositions of the symplectic ball.








24.11.2021, 14:10 (Wednesday) Gerhard Knieper (Ruhr University Bochum)



Title: Growth rate of closed geodesics on surfaces without conjugate points.
Location: Zoom session, the link is available upon request by email



Abstract: Let (M,g) be a closed Riemannian surface of of genus at least 2 and no
conjugate points. By the uniformization theorem such a surface admits
a metric of negative curvature and therefore the topological entropy h
of the geodesic flow is positive. Denote by P(t)  the number of free
homotopy classes  containing a closed geodesic of period $\le t $. We
will show: P(t) is asymptotically equivalent to e^(ht)/(ht) =F(t), i.e.
the ratio of P and F  converges to 1 as t tends to infinity.
An important ingredient in the proof is a mixing flow invariant measure
given by the unique measure of maximal entropy. Under suitable hyperbolicity
assumptions this result carries over to closed Riemannian manifolds without
conjugate and higher dimension.

For closed manifolds of negative curvature the above estimate is well known
and has been originally obtained by Margulis. In a recent preprint
the estimate has been also obtained by Ricks for  certain closed manifolds
(rank 1 mflds) of non-positive curvature. This is a joint work with Vaughn
Climenhaga and Khadim War.








01.12.2021, 14:10 (Wednesday) Sara Tukachinsky (Tel Aviv University)



Title: Bounding chains as a tool in open Gromov-Witten theory
Location: Zoom session, the link is available upon request by email



Abstract: Moduli spaces of J-holomorphic disks have boundary. This interferes with
desirable structures, such as Lagrangian Floer theory or open Gromov-Witten
invariants. One tool for balancing out boundary contributions is a bounding
chain. In this talk I will give some background on the problem, then discuss
in detail what bounding chains are, how they can be constructed, and how
they are used to define invariants.
The work of several people will be mentioned, among them a joint work
with J. Solomon.








08.12.2021, 14:10 (Wednesday) Louis Ioos (Max Planck Institute)



Title: Quantization in stages and canonical metrics
Location: Zoom session, the link is available upon request by email



Abstract: In this talk, I will introduce the notion of quantization in stages, which
lies at the basis of fundamental physical set-ups such as the Stern-Gerlach
experiment, and explain how it can be realized over compact symplectic phase
spaces via the use of Berezin-Toeplitz quantization of vector bundles. In
particular, I will introduce and show how to compute the associated quantum
noise. I will then describe an application to Hermite-Einstein metrics on
stable vector bundles over a projective manifold, and if time permits, I will
show how a refinement of these results in the case of the trivial line bundle
can be applied to Kähler metrics of constant scalar curvature.








15.12.2021, 14:10 (Wednesday) Philippe Charron (Technion)




Title: TBA
Location: Zoom session, the link is available upon request by email



Abstract: TBA







22.12.2021, 17:10 (Wednesday) Simion Filip (University of Chicago)
(PLEASE NOTE CHANGE IN TIME!)




Title: TBA
Location: Zoom session, the link is available upon request by email



Abstract: TBA







05.01.2022, 14:10 (Wednesday) Igor Uljarević (University of Belgrade)



Title: TBA
Location: Zoom session, the link is available upon request by email



Abstract: TBA







02.03.2022, 14:10 (Wednesday) Joé Brendel (University of Neuchâtel)



Title: TBA
Location: Zoom session, the link is available upon request by email



Abstract: TBA







09.03.2022, 14:10 (Wednesday) TBA



Title: TBA
Location: Zoom session, the link is available upon request by email



Abstract: TBA







16.03.2022, 14:10 (Wednesday) TBA



Title: TBA
Location: Zoom session, the link is available upon request by email



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23.03.2022, 14:10 (Wednesday) TBA




Title: TBA
Location: Zoom session, the link is available upon request by email



Abstract: TBA







30.03.2022, 14:10 (Wednesday) TBA



Title: TBA
Location: Zoom session, the link is available upon request by email



Abstract: TBA







06.04.2022, 14:10 (Wednesday) Sheng-Fu Chiu (Institute of Mathematics, Academia Sinica, Taiwan)



Title: From Energy-Time Uncertainty to Symplectic Displacement Energy
Location: Zoom session, the link is available upon request by email



Abstract: Heisenberg's Uncertainty Principle is one of the most celebrated features of
quantum mechanics, which states that one cannot simultaneously obtain the
precise measurements of two conjugated physical quantities such as the pair
of position and momentum or the pair of electric potential and charge density.
Among the different formulations of this fundamental quantum property, the
uncertainty between energy and time has a special place. This is because the
time is rather a variable parametrizing the system evolution than a physical
quantity waiting for determination. Physicists working on the foundation of
quantum theory have understood this energy-time relation by a universal bound
of how fast any quantum system with given energy can evolve from one state to
another in a distinguishable (orthogonal) way. Recently, there have been many
arguing that this bound is not a pure quantum phenomenon but a general
dynamical property of Hilbert space. In this talk, in contrast to the usual
Hilbert space formalism, we will provide a homological viewpoint of this
evolutional speed limit based on a persistence-like distance of the derived
category of sheaves : during a time period what is the minimal energy needed
for a system to evolve from one sheaf to a status that is distinguishable from
a given subcategory? As an application, we will also discuss its geometric
incarnation in the dynamics of classical mechanics, namely the notion of
symplectic displacement. We will see how this categorical energy manages to
characterize the symplectic energy for disjointing a Lagrangian from an open set.








27.04.2022, 14:10 (Wednesday) TBA



Title: TBA
Location: Zoom session, the link is available upon request by email



Abstract: TBA







11.05.2022, 14:10 (Wednesday) TBA



Title: TBA
Location: Zoom session, the link is available upon request by email



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18.05.2022, 14:10 (Wednesday) TBA



Title: TBA
Location: Zoom session, the link is available upon request by email



Abstract: TBA







25.05.2022, 14:10 (Wednesday) TBA



Title: TBA
Location: Zoom session, the link is available upon request by email



Abstract: TBA







01.06.2022, 14:10 (Wednesday) TBA



Title: TBA
Location: Zoom session, the link is available upon request by email



Abstract: TBA







08.06.2021, 14:10 (Wednesday) TBA



Title: TBA
Location: Zoom session, the link is available upon request by email



Abstract: TBA








Organized by Misha Bialy, Lev Buhovsky, Yaron Ostrover, and Leonid Polterovich