





21.10.2020, 14:10 (Wednesday) 
Laurent Charles (Sorbonne University, Paris),
Yohann Le Floch (University of Strasbourg) 




Title: 
Quantum
propagation for BerezinToeplitz operators 

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




Abstract: 
The
relationship between quantum propagation, defined from
Schrödinger
equation, and Hamiltonian dynamics is a classical theme
of semiclassical
analysis. More generally, Lagrangian manifolds play an
important role
in our understanding of quantum mechanics. We will
present several
results illustrating this in the context of quantization
of a complex
compact phase space. 









28.10.2020, 14:10
(Wednesday)

Andrew Lobb (Durham University)





Title:

The rectangular peg problem 

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




Abstract: 
For any smooth Jordan curve and rectangle in the
plane, we show that
there exist four points on the Jordan curve forming the
vertices of a
rectangle similar to the given one. Joint work with Josh
Greene.










04.11.2020, 17:10 (Wednesday)
(PLEASE
NOTE CHANGE IN TIME!)

Laszlo Lempert (Purdue University) 




Title: 
On the adjoint action of symplectomorphism groups


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




Abstract: 
Motivated by constructions in Kähler geometry, in
this talk we consider
a compact symplectic manifold $(X,\omega)$ and the group
$G$ of its
symplectomorphisms. We study the action of $G$ on the
Fréchet space
$C^\infty(X)$ of smooth functions, by pullback, and
describe properties of
convex functions $p:C^\infty(X)\to\mathbb R$ that are
invariant under this
action.









11.11.2020, 14:10 (Wednesday)

Bo Berndtsson (Chalmers University of Technology) 




Title: 
Complex integrals and Kuperberg's proof of the
BourgainMilman theorem 

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




Abstract: 
I will show a function version of the
BourgainMilman theorem:
$$ \int e^{\phi}\int e^{\phi^*}\geq \pi^n $$,
if $\phi$ is a symmetric convex function on $\R^n$
and $\phi^*$ is its
Legendre transform. The proof is inspired by Kuperberg's
proof of the
BourgainMilman theorem but uses complex analytic
techniques. 









18.11.2020, 14:10 (Wednesday) 
Misha Bialy (Tel Aviv
University)





Title: 
The BirkhoffPoritsky conjecture for
centrallysymmetric billiard tables 

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




Abstract: 
In this talk (joint work with
A.E. Mironov) I shall discuss a recent
proof of the BirkhoffPoritsky conjecture for
centrallysymmetric
C^2smooth convex planar billiards. We assume that the
domain between
the invariant curve of 4periodic orbits and the
boundary of the phase
cylinder is foliated by C^0invariant curves. Under this
assumption we
prove that the billiard curve is an ellipse. The main
ingredients of
the proof are : (1) the nonstandard generating function
for convex
billiards; (2) the remarkable structure of the invariant
curve
consisting of 4periodic orbits; and (3) the
integralgeometry
approach initiated for rigidity results of circular
billiards.
Surprisingly, our result yields a Hopftype rigidity for
billiard
in ellipse.










25.11.2020, 14:10 (Wednesday) 
Frol Zapolsky (University of Haifa) 




Title: 
Relative symplectic cohomology and idealvalued
measures 

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




Abstract: 
In a joint work in progress together with A.
Dickstein, Y. Ganor, and
L. Polterovich we prove new symplectic rigidity results.
First, we
categorify the notion of a heavy subset of a symplectic
manifold (due
to EntovPolterovich), and in particular provide a
simple algebraic
criterion which guarantees that two heavy sets
intersect. Next, we
treat involutive maps defined on a symplectic manifold
M; a smooth
map M > B is involutive if pullbacks of smooth
functions on B Poisson
commute. For such maps we prove a refinement of
EntovPolterovich's
nondisplaceable fiber theorem, as well as a symplectic
Tverbergtype
theorem, which roughly says that each involutive map
into a manifold
of sufficiently low dimension has a fiber which
intersects a wide
family of subsets of M.
All of these results are proved using a generalized
version of Gromov's
notion of idealvalued measures, which furnish an easily
digestible
way to package the relevant information. We construct
such measures
using relative symplectic cohomology, an invariant
recently introduced
by U. Varolgunes, who also proved the MayerVietoris
property for it,
on which our work relies in a crucial manner. Our main
technical
innovation is the relative symplectic cohomology of a
pair, whose
construction is inspired by homotopy theory. 









02.12.2020, 17:10 (Wednesday)
(PLEASE
NOTE CHANGE IN TIME!)

Vinicius G. B. Ramos (IMPA, Brazil) 




Title: 
Examples around the strong Viterbo conjecture 

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




Abstract: 
The Viterbo conjecture states that the ball
maximizes any normalized
symplectic capacity within all convex sets in R^{2n} of
a fixed volume
and that it is the unique maximizer. A stronger
conjecture says that
all normalized capacities coincide for convex sets. In
joint work with
Gutt and Hutchings, we prove the stronger conjecture for
a somewhat
different class of 4dimensional domains, namely toric
domains with a
dynamically convex toric boundary. In joint work with
Ostrover and Sepe,
we prove that a 4dimensional Lagrangian product which
is a maximizer
of the HoferZehnder capacity is nontrivially
symplectomorphic to a
ball giving further evidence to the uniqueness claim of
Viterbo's
conjecture. In this talk, I will explain the proof of
these two results. 









09.12.2020, 14:10 (Wednesday) 
Lev Birbrair (Universidade Federal do Ceará,
Brazil) 




Title: 
Lipschitz geometry of surface germs in $\R^4$:
metric knots 

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




Abstract: 
A link at the origin of an
isolated singularity of a twodimensional
semialgebraic surface in $\R^4$ is a topological knot
(or link) in $S^3$.
We study the connection between the ambient Lipschitz
geometry of
semialgebraic surface germs in $\R^4$ and the knot
theory. Namely, for
any knot $K$, we construct a surface $X_K$ in $\R^4$
such that: $X_K$
has a trivial knot at the origin; the germs $X_K$ are
outer biLipschitz
equivalent for all $K$; two germs $X_{K}$ and $X_{K'}$
are ambient
biLipschitz equivalent only if the knots $K$ and $K'$
are isotopic.










16.12.2020, 14:10 (Wednesday) 
Barak Weiss (Tel Aviv University)





Title: 
Ergodicity of rel foliations on the space of
holomorphic one forms 

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




Abstract: 
The rel foliation is a foliation of the moduli
space of abelian
differentials obtained by "moving the zeroes of the one
form while
keeping all absolute periods fixed". It has been studied
in complex
analysis and dynamics under different names (isoperiodic
foliation,
Schiffer variation, kernel foliation). Until recent
years the question
of its ergodicity was wide open. Recently partial
results were obtained
by CalsamigliaDeroinFrancaviglia and by Hamenstadt. In
our work we
completely resolve the ergodicity question. Joint work
in progress with
Jon Chaika and Alex Eskin, based on a farreaching
extension of a
celebrated result of Eskin and Mirzakhani. All
relevant notions will
be explained in the lecture and no prior familiarity
with dynamics on
spaces of one forms will be assumed. 









23.12.2020, 14:10 (Wednesday) 
Ood Shabtai (Tel
Aviv University) 




Title: 
On polynomials in two spectral projections of
spin operators 

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




Abstract: 
We discuss the semiclassical behavior of an
arbitrary bivariate
polynomial evaluated on a pair of spectral projections
of spin
operators, and compare it with its value on a pair of
random
projections. 









30.12.2020, 14:10 (Wednesday) 
Shira Tanny (Tel Aviv University) 




Title: 
A maxinequality for spectral invariants of
disjointly supported Hamiltonians 

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




Abstract: 
The relation between spectral invariants of
disjointly supported
Hamiltonians and that of their sum was studied by
Humiliere, Le Roux
and Seyfaddini on aspherical manifolds. We study this
relation in a
wider setting and derive applications to Polterovich's
Poisson bracket
invariant. This is a work in progress. 









06.01.2021, 14:10 (Wednesday) 
Vincent Humilière (Sorbonne University) 




Title: 
Is the group of compactly supported area
preserving homeomorphisms of the 2disk simple? 

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




Abstract: 
This long standing open problem has been recently
solved in joint work
with Dan CristofaroGardiner and Sobhan Seyfaddini. I
will present some
background and the main ideas that lead to the proof. It
is based on
tools from symplectic topology and more precisely on a
theory due to
Hutchings, called Periodic Floer Homology. 









13.01.2021, 14:00 (Wednesday)

Dan Mangoubi (The Hebrew University of Jerusalem)





Title: 
A Local version of Courant's Nodal domain Theorem


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




Abstract: 
Let u_k be an eigenfunction of a vibrating string
(with fixed ends)
corresponding to the kth eigenvalue. It is not
difficult to show that
the number of zeros of u_k is exactly k+1. Equivalently,
the number of
connected components of the complement of $u_k=0$ is
$k$.
In 1923 Courant found that in higher dimensions
(considering eigenfunctions
of the Laplacian on a closed Riemannian manifold M) the
number of connected
components of the open set $M\setminus {u_k=0}$ is at
most $k$.
In 1988 Donnelly and Fefferman gave a bound on the
number of connected
components of $B\setminus {u_k=0}$, where $B$ is a ball
in $M$. However,
their estimate was not sharp (even for spherical
harmonics).
We describe the ideas which give the sharp bound on the
number of connected
components in a ball. The talk is based on a joint work
with S. Chanillo,
A. Logunov and E. Malinnikova, with a contribution due
to F. Nazarov. 









03.03.2021, 14:10 (Wednesday) 
Boaz Klartag (Weizmann Institute of Science) 




Title: 
Rigidity of Riemannian embeddings of discrete
metric spaces 

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




Abstract: 
Let M be a complete, connected Riemannian surface
and
suppose that S is a discrete subset of M. What can we
learn about M
from the knowledge of all distances in the surface
between pairs of
points of S? We prove that if the distances in S
correspond to the
distances in a 2dimensional lattice, or more generally
in an
arbitrary net in R^2, then M is isometric to the
Euclidean plane. We
thus find that Riemannian embeddings of certain discrete
metric spaces
are rather rigid. A corollary is that a subset of Z^3
that strictly
contains a twodimensional lattice cannot be
isometrically embedded in
any complete Riemannian surface. This is a joint work
with M. Eilat. 









10.03.2021, 14:10 (Wednesday) 
Daniel CristofaroGardiner (IAS Princeton;
University of California, Santa Cruz) 




Title: 
The subleading asymptotics of the ECH spectrum


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




Abstract: 
Embedded contact homology can be used to
associate a sequence of spectral
invariants, called ECH spectral invariants, to any
closed threemanifold
with a contact form. In previous joint work, we
proved a “Volume Property”
that recovers the volume of any such manifold from the
asymptotics of its
ECH spectral invariants. I will discuss recent
work aimed at better
understanding the subleading asymptotics of this
sequence. The main
subject of my talk will be a joint work with Nikhil
Savale in which we
prove a new bound on the growth rate of the subleading
asymptotics.
I will also briefly mention a conjecture, due to
Hutchings, concerning
recovering the “contact Ruelle invariant” from the
subleading asymptotics. 









17.03.2021, 14:10 (Wednesday) 
Dmitry Faifman (Tel Aviv University) 




Title: 
Around the Funk metric and its billiards 

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




Abstract: 
The Funk metric in the interior of a convex body
is a lesser known
relative of the projectivelyinvariant Hilbert metric,
yet in some
ways simpler and more natural. Starting with a few
simple observations,
we will explore some Funkinspired generalizations of
wellknown
results in the geometry of normed spaces and Minkowski
billiards,
such as Schäffer's dual girth conjecture and the
GutkinTabachnikov
duality. I will also offer a Funk approach to the
integrability of the
hyperbolic billiard in a conic. Time permitting, I will
discuss the
volume of metric balls in Funk geometry, leading to a
generalization
of the BlaschkeSantalo inequality. 









24.03.2021, 14:10 (Wednesday) 
Daniel PeraltaSalas (ICMAT
Madrid) 




Title: 
Turing completeness and universality of steady
Euler flows 

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




Abstract: 
I will review recents results on the Turing
completeness and universality
of steady solutions to the Euler equations. In
particular, I will show
the existence of threedimensional fluid flows
exhibiting undecidable
trajectories and discuss other universality features
such as embeddability
of diffeomorphisms into steady Euler states. These
results are motivated by
Tao's programme to address the blowup problem for the
NavierStokes
equations based on the Turing completeness of the fluid
flows. This is
based on joint works with Robert Cardona, Eva Miranda
and Francisco Presas. 









07.04.2021, 14:10 (Wednesday) 
Daniel Rosen (RuhrUniversität Bochum) 




Title: 
Random inscribed polytopes in NonEuclidean
Geometries 

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




Abstract: 
Random polytopes have a long history, going back
to Sylvester's famous
fourpoint problem. Since then their study has become a
mainstream topic
in convex and stochastic geometry, with close connection
to polytopal
approximation problems, among other things. In this talk
we will consider
random polytopes in constant curvature geometries, and
show that their
volume satisfies a central limit theorem. The proof uses
Stein's method
for normal approximation, and extends to general
projective Finsler metrics. 









21.04.2021, 14:10 (Wednesday) 
Thomas Melistas (University of Georgia) 




Title: 
The LargeScale Geometry of Overtwisted Contact
Forms 

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




Abstract: 
Inspired by the symplectic BanachMazur distance,
proposed by Ostrover
and Polterovich in the setting of nondegenerate
starshaped domains of
Liouville manifolds, we define a distance on the space
of contact forms
supporting a given contact structure on a closed contact
manifold. We
compare it to a recently defined contact BanachMazur
distance by Rosen
and Zhang and we use it in order to biLipschitz embed
part of the
2dimensional Euclidean space into the space of
overtwisted contact
forms supporting a given contact structure on a smooth
closed manifold. 









28.04.2021, 14:10 (Wednesday) 
Zvi ShemTov (The Hebrew University of Jerusalem) 




Title: 
Conjugationinvariant norms on arithmetic groups 

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




Abstract: 
A classical theorem of Ostrowski says that every
absolute value on the
field of rational numbers, or equivalently on the ring
of integers, is
equivalent to either the standard (real) absolute value,
or a $p$adic
absolute value, for which the closure of the integers is
compact. In
this talk we will see a nonabelian analogue of this
result for
$SL(n\ge3,\Z)$, and related groups of arithmetic type.
We will see
a relation to the celebrated Margulis' normal subgroup
theorem, and
derive rigidity results for homomorphisms into certain
nonlocally
compact groups  those endowed with a biinvariant
metric. We will
also discuss a relation to the deep work of
NikolovSegal on profinite
groups. This is a joint work with Leonid Polterovich and
Yehuda Shalom.










05.05.2021, 14:10 (Wednesday) 
Otto van Koert (Seoul National University)





Title: 
A generalization of the
PoincareBirkhoff fixed point theorem and the restricted
threebody problem 

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




Abstract: 
In joint work with Agustin Moreno, we propose a
generalization of the
PoincareBirkhoff fixed point theorem. We start with a
construction of
global hypersurfaces of section in the spatial
threebody problem, describe
some return maps and suggest some generalizations of the
PoincareBirkhoff
fixed point theorem. We use symplectic homology in the
proof of our theorem. 









12.05.2021, 14:10 (Wednesday) 
Georgios Dimitroglou Rizell (Uppsala University) 




Title: 
Nondegeneracy of Legendrians from bifurcation of
contact homology 

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




Abstract: 
We show that the invariance of Legendrian contact
homology can be
formulated in terms of a bifurcation analysis whose
action properties
are continuous with respect to the oscillatory norm of
the contact
Hamiltonian. (I.e. the barcode varies continuously with
respect to
the same.) Combined with work of RosenZhang this
implies nondegeneracy
of the ShelukhinChekanovHofer metric on the space of
Legendrian
embeddings. We also explain how convex surface
techniques in dimension
three can be used to prove a statement related to the
converse: a
nonLegendrian knot cannot be approximated by the image
of a Legendrian
knot under a sequence of C0converging
contactomorphisms. This is joint
work with M. Sullivan.










19.05.2021, 14:10 (Wednesday) 
Luis Diogo (Fluminense Federal University,
Brazil) 




Title: 
Monotone Lagrangians in cotangent bundles of
spheres 

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




Abstract: 
Among all Lagrangian submanifolds of a symplectic
manifold, the class of
monotone Lagrangians is often very rich and nicely
suited to being studied
using pseudoholomophic curves. We find a family of
monotone Lagrangians
in cotangent bundles of spheres with the following
property: every compact
monotone Lagrangian with nontrivial Floer cohomology
cannot be displaced
by a Hamiltonian diffeomorphism from at least one
element in the family.
This follows from the fact that the Lagrangians in the
family splitgenerate
the compact monotone Fukaya category. This is joint work
with Mohammed Abouzaid. 









26.05.2021, 14:10 (Wednesday) 
Jonathan David Evans (Lancaster University)





Title: 
TBA 

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




Abstract: 
TBA 









02.06.2021, 14:10 (Wednesday) 
Jeff Hicks (University of Cambridge) 




Title: 
TBA 

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




Abstract: 
TBA 












09.06.2021, 14:10 (Wednesday) 
Itamar Rosenfeld Rauch (Technion, Haifa) 




Title: 
TBA


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




Abstract: 
TBA










16.06.2021,
14:10 (Wednesday) 
Marcelo
R.R. Alves (University of Antwerp) 




Title: 
TBA


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




Abstract: 
TBA 





