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| 21.10.2020, 14:10 (Wednesday) |
Laurent Charles (Sorbonne University, Paris),
Yohann Le Floch (University of Strasbourg) |
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| Title: |
Quantum
propagation for Berezin-Toeplitz operators |
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| Location: |
Zoom session, the link is available upon request
by email |
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| Abstract: |
The
relationship between quantum propagation, defined from
Schrödinger
equation, and Hamiltonian dynamics is a classical theme
of semi-classical
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. |
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28.10.2020, 14:10
(Wednesday)
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Andrew Lobb (Durham University)
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Title:
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The rectangular peg problem |
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| Location: |
Zoom session, the link is available upon request
by email |
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| 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.
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04.11.2020, 17:10 (Wednesday)
(PLEASE
NOTE CHANGE IN TIME!)
|
Laszlo Lempert (Purdue University) |
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| Title: |
On the adjoint action of symplectomorphism groups
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|
| Location: |
Zoom session, the link is available upon request
by email |
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| 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.
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11.11.2020, 14:10 (Wednesday)
|
Bo Berndtsson (Chalmers University of Technology) |
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| Title: |
Complex integrals and Kuperberg's proof of the
Bourgain-Milman theorem |
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| Location: |
Zoom session, the link is available upon request
by email |
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| Abstract: |
I will show a function version of the
Bourgain-Milman 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
Bourgain-Milman theorem but uses complex analytic
techniques. |
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| 18.11.2020, 14:10 (Wednesday) |
Misha Bialy (Tel Aviv
University)
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| Title: |
The Birkhoff-Poritsky conjecture for
centrally-symmetric billiard tables |
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| Location: |
Zoom session, the link is available upon request
by email |
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| Abstract: |
In this talk (joint work with
A.E. Mironov) I shall discuss a recent
proof of the Birkhoff-Poritsky conjecture for
centrally-symmetric
C^2-smooth convex planar billiards. We assume that the
domain between
the invariant curve of 4-periodic orbits and the
boundary of the phase
cylinder is foliated by C^0-invariant curves. Under this
assumption we
prove that the billiard curve is an ellipse. The main
ingredients of
the proof are : (1) the non-standard generating function
for convex
billiards; (2) the remarkable structure of the invariant
curve
consisting of 4-periodic orbits; and (3) the
integral-geometry
approach initiated for rigidity results of circular
billiards.
Surprisingly, our result yields a Hopf-type rigidity for
billiard
in ellipse.
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| 25.11.2020, 14:10 (Wednesday) |
Frol Zapolsky (University of Haifa) |
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| Title: |
Relative symplectic cohomology and ideal-valued
measures |
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| Location: |
Zoom session, the link is available upon request
by email |
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| 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 Entov-Polterovich), 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
Entov-Polterovich's
nondisplaceable fiber theorem, as well as a symplectic
Tverberg-type
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 ideal-valued 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 Mayer-Vietoris
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. |
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02.12.2020, 17:10 (Wednesday)
(PLEASE
NOTE CHANGE IN TIME!)
|
Vinicius G. B. Ramos (IMPA, Brazil) |
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| Title: |
Examples around the strong Viterbo conjecture |
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| Location: |
Zoom session, the link is available upon request
by email |
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| 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 4-dimensional domains, namely toric
domains with a
dynamically convex toric boundary. In joint work with
Ostrover and Sepe,
we prove that a 4-dimensional Lagrangian product which
is a maximizer
of the Hofer-Zehnder capacity is non-trivially
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. |
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| 09.12.2020, 14:10 (Wednesday) |
Lev Birbrair (Universidade Federal do Ceará,
Brazil) |
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| Title: |
Lipschitz geometry of surface germs in $\R^4$:
metric knots |
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| Location: |
Zoom session, the link is available upon request
by email |
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| Abstract: |
A link at the origin of an
isolated singularity of a two-dimensional
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 bi-Lipschitz
equivalent for all $K$; two germs $X_{K}$ and $X_{K'}$
are ambient
bi-Lipschitz equivalent only if the knots $K$ and $K'$
are isotopic.
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| 16.12.2020, 14:10 (Wednesday) |
Barak Weiss (Tel Aviv University)
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| Title: |
Ergodicity of rel foliations on the space of
holomorphic one forms |
|
| Location: |
Zoom session, the link is available upon request
by email |
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| 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 Calsamiglia-Deroin-Francaviglia 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 far-reaching
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. |
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| 23.12.2020, 14:10 (Wednesday) |
Ood Shabtai (Tel
Aviv University) |
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| Title: |
On polynomials in two spectral projections of
spin operators |
|
| Location: |
Zoom session, the link is available upon request
by email |
|
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| 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. |
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| 30.12.2020, 14:10 (Wednesday) |
Shira Tanny (Tel Aviv University) |
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| Title: |
A max-inequality for spectral invariants of
disjointly supported Hamiltonians |
|
| Location: |
Zoom session, the link is available upon request
by email |
|
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| 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. |
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| 06.01.2021, 14:10 (Wednesday) |
Vincent Humilière (Sorbonne University) |
|
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| Title: |
Is the group of compactly supported area
preserving homeomorphisms of the 2-disk simple? |
|
| Location: |
Zoom session, the link is available upon request
by email |
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| Abstract: |
This long standing open problem has been recently
solved in joint work
with Dan Cristofaro-Gardiner 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. |
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13.01.2021, 14:00 (Wednesday)
|
Dan Mangoubi (The Hebrew University of Jerusalem)
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| Title: |
A Local version of Courant's Nodal domain Theorem
|
|
| Location: |
Zoom session, the link is available upon request
by email |
|
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|
|
| Abstract: |
Let u_k be an eigenfunction of a vibrating string
(with fixed ends)
corresponding to the k-th 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. |
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| 03.03.2021, 14:10 (Wednesday) |
Boaz Klartag (Weizmann Institute of Science) |
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| Title: |
Rigidity of Riemannian embeddings of discrete
metric spaces |
|
| Location: |
Zoom session, the link is available upon request
by email |
|
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| 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 2-dimensional 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 two-dimensional lattice cannot be
isometrically embedded in
any complete Riemannian surface. This is a joint work
with M. Eilat. |
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| 10.03.2021, 14:10 (Wednesday) |
Daniel Cristofaro-Gardiner (IAS Princeton;
University of California, Santa Cruz) |
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| Title: |
The subleading asymptotics of the ECH spectrum
|
|
| Location: |
Zoom session, the link is available upon request
by email |
|
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|
| Abstract: |
Embedded contact homology can be used to
associate a sequence of spectral
invariants, called ECH spectral invariants, to any
closed three-manifold
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. |
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| 17.03.2021, 14:10 (Wednesday) |
Dmitry Faifman (Tel Aviv University) |
|
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|
| 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 projectively-invariant Hilbert metric,
yet in some
ways simpler and more natural. Starting with a few
simple observations,
we will explore some Funk-inspired generalizations of
well-known
results in the geometry of normed spaces and Minkowski
billiards,
such as Schäffer's dual girth conjecture and the
Gutkin-Tabachnikov
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 Blaschke-Santalo inequality. |
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| 24.03.2021, 14:10 (Wednesday) |
Daniel Peralta-Salas (ICMAT
Madrid) |
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|
| Title: |
Turing completeness and universality of steady
Euler flows |
|
| Location: |
Zoom session, the link is available upon request
by email |
|
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|
|
| 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 three-dimensional 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 blow-up problem for the
Navier-Stokes
equations based on the Turing completeness of the fluid
flows. This is
based on joint works with Robert Cardona, Eva Miranda
and Francisco Presas. |
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| 07.04.2021, 14:10 (Wednesday) |
Daniel Rosen (Ruhr-Universität Bochum) |
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|
| Title: |
Random inscribed polytopes in Non-Euclidean
Geometries |
|
| Location: |
Zoom session, the link is available upon request
by email |
|
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|
| Abstract: |
Random polytopes have a long history, going back
to Sylvester's famous
four-point 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. |
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| 21.04.2021, 14:10 (Wednesday) |
Thomas Melistas (University of Georgia) |
|
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|
|
| Title: |
The Large-Scale Geometry of Overtwisted Contact
Forms |
|
| Location: |
Zoom session, the link is available upon request
by email |
|
|
|
|
| Abstract: |
Inspired by the symplectic Banach-Mazur distance,
proposed by Ostrover
and Polterovich in the setting of non-degenerate
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 Banach-Mazur
distance by Rosen
and Zhang and we use it in order to bi-Lipschitz embed
part of the
2-dimensional Euclidean space into the space of
overtwisted contact
forms supporting a given contact structure on a smooth
closed manifold. |
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| 28.04.2021, 14:10 (Wednesday) |
Zvi Shem-Tov (The Hebrew University of Jerusalem) |
|
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|
|
| Title: |
Conjugation-invariant norms on arithmetic groups |
|
| Location: |
Zoom session, the link is available upon request
by email |
|
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|
|
| 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 non-abelian 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
non-locally
compact groups -- those endowed with a bi-invariant
metric. We will
also discuss a relation to the deep work of
Nikolov-Segal on profinite
groups. This is a joint work with Leonid Polterovich and
Yehuda Shalom.
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|
| 05.05.2021, 14:10 (Wednesday) |
Otto van Koert (Seoul National University)
|
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|
|
| Title: |
A generalization of the
Poincare-Birkhoff fixed point theorem and the restricted
three-body 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
Poincare-Birkhoff fixed point theorem. We start with a
construction of
global hypersurfaces of section in the spatial
three-body problem, describe
some return maps and suggest some generalizations of the
Poincare-Birkhoff
fixed point theorem. We use symplectic homology in the
proof of our theorem. |
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| 12.05.2021, 14:10 (Wednesday) |
Georgios Dimitroglou Rizell (Uppsala University) |
|
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|
| Title: |
Non-degeneracy of Legendrians from bifurcation of
contact homology |
|
| Location: |
Zoom session, the link is available upon request
by email |
|
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|
|
| 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 Rosen-Zhang this
implies non-degeneracy
of the Shelukhin-Chekanov-Hofer 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
non-Legendrian knot cannot be approximated by the image
of a Legendrian
knot under a sequence of C0-converging
contactomorphisms. This is joint
work with M. Sullivan.
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|
| 19.05.2021, 14:10 (Wednesday) |
Luis Diogo (Fluminense Federal University,
Brazil) |
|
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|
|
| Title: |
Monotone Lagrangians in cotangent bundles of
spheres |
|
| Location: |
Zoom session, the link is available upon request
by email |
|
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|
|
| 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 non-trivial 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 split-generate
the compact monotone Fukaya category. This is joint work
with Mohammed Abouzaid. |
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|
| 26.05.2021, 14:10 (Wednesday) |
Jonathan David Evans (Lancaster University)
|
|
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|
|
| Title: |
A Lagrangian Klein bottle you can't squeeze |
|
| Location: |
Zoom session, the link is available upon request
by email |
|
|
|
|
| Abstract: |
Given a nonorientable Lagrangian surface L in a
symplectic 4-manifold,
how far can you deform the symplectic form before there
is no Lagrangian
surface isotopic to L? I will discuss this problem in
general and explain
the solution in a particular case. |
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|
| 02.06.2021, 14:10 (Wednesday) |
Jeff Hicks (University of Cambridge) |
|
|
|
|
| Title: |
Decompositions of Lagrangian
Cobordisms |
|
| Location: |
Zoom session, the link is available upon request
by email |
|
|
|
|
| Abstract: |
Consider a symplectic manifold X, and its product
with the complex plane X x C.
A Lagrangian cobordism is a Lagrangian submanifold in X
x C whose noncompact
ends suitably limit to Lagrangian submanifolds of X. In
this talk, we'll discuss
how every Lagrangian submanifold can be decomposed into
some simple pieces -
surgery traces and suspensions of exact homotopy.
Furthermore, we'll speculate
about the connection between these decompositions and
the work of Biran and Cornea
relating Lagrangian cobordisms to equivalences of
Lagrangian Floer cohomology. |
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|
| 09.06.2021, 14:10 (Wednesday) |
Itamar Rosenfeld Rauch (Technion, Haifa) |
|
|
|
|
| Title: |
On the Hofer Girth of the
Sphere of Great Circles
|
|
| Location: |
Zoom session, the link is available upon request
by email |
|
|
|
|
| Abstract: |
An equator of
 is
an embedded circle that divides the sphere into two
equal area discs. Chekanov introduced a distance
function on the space of
equators, induced by the Hofer norm. We define the Hofer
girth of this
space, roughly speaking, as the smallest diameter of a
non-contractible
sphere in this space, as inspired by the classic metric
invariant of systoles.
A somewhat natural embedding of
in
the space of equators sends each
point to the great circle perpendicular to it; this
embedding is called the
sphere of great circles.
In this talk we will discuss a few properties of Hofer
girth, and show that
the diameter of the sphere of great circles is not
optimal, by constructing
a strictly better candidate.
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|
| 16.06.2021,
14:10 (Wednesday) |
Marcelo
R.R. Alves (University of Antwerp) |
|
|
|
|
| Title: |
Entropy
collapse versus entropy rigidity for Reeb and Finsler
flows
|
|
| Location: |
Zoom
session, the link is available upon request by email |
|
|
|
|
| Abstract: |
The
topological entropy of a flow on a compact manifold is a
measure
of complexity related to many other notions of growth.
By celebrated
works of Katok and Besson-Courtois-Gallot, the
topological entropy
of geodesic flows of Riemannian metrics with a fixed
volume on a
manifold M that carries a metric of negative curvature
is uniformly
bounded from below by a positive constant depending only
on M. We show
that this result persists for all (possibly
irreversible) Finsler
flows, but that on every closed contact manifold there
exists a Reeb
flow of fixed volume and arbitrarily small entropy. This
is joint work
with Alberto Abbondandolo, Murat Saglam and Felix
Schlenk. |
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