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| 06.11.2024, 14:10 (Wednesday) |
Orientation
meeting for students |
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| Location: |
Schreiber
bldg., room 309, Tel-Aviv University |
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13.11.2024, 14:10
(Wednesday)
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Dylan Cant (Université Paris-Saclay)
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Title:
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Spectral invariants and eternal classes in
symplectic cohomology |
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| Location: |
Zoom session and screening in Schreiber 309
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| 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.
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| 20.11.2024, 14:10 (Wednesday) |
Shira Tanny (Weizmann Institute of Science)
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| Title: |
From Gromov–Witten theory to the closing lemma
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| Location: |
Schreiber 309
and zoom session |
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| 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.
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27.11.2024, 14:10 (Wednesday)
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Andrew Lobb (Durham University) |
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| Title: |
Symplectic topology and peg problems |
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| Location: |
Zoom session
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| 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. |
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| 04.12.2024, 14:10 (Wednesday) |
Peter Albers (Heidelberg
University) |
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| Title: |
Outer symplectic billiard |
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| Location: |
Zoom session and screening in Schreiber 309
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| 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.
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| 11.12.2024, 14:10 (Wednesday) |
Marcelo Atallah (University of Sheffield) |
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| Title: |
The number of periodic points of surface
symplectomorphisms |
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| Location: |
Zoom session and screening in Schreiber 309 |
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| 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. |
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| 18.12.2024, 14:10 (Wednesday) |
Stefan Nemirovski (Steklov Mathematical Institute
and Ruhr University Bochum) |
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| Title: |
Unknotting Lagrangian
in
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| Location: |
Zoom session and screening in Schreiber 309 |
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| Abstract: |
The purpose of the talk is to describe the
classification of
Lagrangian embeddings of
in the standard
symplectic space
up to smooth isotopy for
all
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| 25.12.2024, 14:10 (Wednesday) |
Jake Solomon (Hebrew University of Jerusalem) |
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| Title: |
Toward open mirror symmetry for Fano manifolds |
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| Location: |
Schreiber 309
and zoom session
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| 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.
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| 01.01.2025, 14:10 (Wednesday) |
Snir Ben Ovadia (Pennsylvania
State University) |
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| Title: |
Exponential
volume limits |
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| Location: |
Schreiber 309
and zoom session |
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| 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. |
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| 08.01.2025, 14:10 (Wednesday) |
Marcelo R.R. Alves
(University of Antwerp) |
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| Title: |
From curve shortening to Birkhoff sections of
geodesic flows |
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| Location: |
Zoom session and screening in Schreiber 309 |
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| 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. |
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| 15.01.2025, 14:10 (Wednesday) |
Yaniv Ganor (Holon Institute of Technology)
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| Title: |
Persistence in Wrapped Floer Homology and Poisson
Bracket Invariants |
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| Location: |
Schreiber 309
and zoom session |
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| 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. |
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| 22.01.2025, 14:10 (Wednesday) |
Emmanuel Opshtein (University of Strasbourg)
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| Title: |
Symplectic/contact rigidity of some
Lagrangian/Legendrian skeleta in dimension 4 |
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| Location: |
Zoom session and screening in Schreiber 309 |
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| 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. |
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29.01.2025, 14:10 (Wednesday)
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Michael Entov (Technion) |
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| Title: |
New geometric measurements of Legendrian
isotopies |
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| Location: |
Schreiber 309
and zoom session |
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| 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. |
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19.03.2025,
14:10 (Wednesday)
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Daniel
Tsodikovich (ISTA) |
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| Title: |
Local
rigidity of integrable symplectic billiards |
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| Location: |
Schreiber 309
and zoom session |
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| 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. |
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| 26.03.2025, 16:10 (Wednesday) |
Vukašin Stojisavljević (University of Montreal) |
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| Title: |
On certain C^0-aspects of contactomorphism groups
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| Location: |
Zoom session
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| 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.
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| 02.04.2025, 14:10 (Wednesday) |
Isabelle Charton (Tel Aviv University) |
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| Title: |
Monotone Symplectic Manifolds with a Torus Action
of Complexity One |
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| Location: |
Schreiber bldg., room 309, Tel Aviv University
(and online via zoom). |
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| Abstract: |
A compact symplectic manifold
is called
positive monotone if its first Chern class is a
positive
multiple of
in the second de Rham group
.
A Fano variety is a smooth complex variety that
admits a
holomorphic embedding into
for some
.
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
.
In
particular, I will present new results for the case
where the
complexity of the action is one, i.e.,
.
This talk is based on joint work with Liat Kessler,
Silvia Sabatini,
and Daniele Sepe. |
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| 23.04.2025, 14:10 (Wednesday) |
Oliver Edtmair (ETH Zürich) |
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| Title: |
Volume filling ellipsoids |
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| Location: |
Zoom session and screening in Schreiber 309 |
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| 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. |
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| 07.05.2025, 14:10 (Wednesday) |
Rei Henigman (Tel Aviv University)
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| Title: |
Classification of symplectic non-Hamiltonian
circle actions on 4-manifolds |
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| Location: |
Schreiber bldg., room 309, Tel Aviv University
(and online via zoom). |
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| 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. |
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| 14.05.2025, 14:10 (Wednesday) |
Erman Çineli (ETH Zürich) |
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| Title: |
TBA |
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| Location: |
TBA |
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| Abstract: |
TBA |
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| 21.05.2025, 14:10 (Wednesday) |
Stefan Matijević (Ruhr University Bochum) |
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| Title: |
TBA |
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| Location: |
TBA |
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| Abstract: |
TBA |
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| 28.05.2025, 14:10 (Wednesday) |
Yoel Groman (Hebrew University of Jerusalem) |
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| Title: |
TBA |
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| Location: |
TBA |
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| Abstract: |
TBA |
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| 04.06.2025, 14:10 (Wednesday) |
Umberto Hryniewicz (RWTH Aachen University) |
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| Title: |
TBA |
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| Location: |
TBA |
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| Abstract: |
TBA |
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| 11.06.2025, 14:10 (Wednesday) |
Joe Brendel (ETH Zürich) |
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| Title: |
TBA |
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| Location: |
TBA |
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| Abstract: |
TBA |
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| 18.06.2025, 14:10 (Wednesday) |
Michael Brandenbursky (BGU) |
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| Title: |
TBA |
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| Location: |
TBA |
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| Abstract: |
TBA |
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| 25.06.2025, 14:10 (Wednesday) |
TBA |
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| Title: |
TBA |
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| Location: |
TBA |
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| Abstract: |
TBA |
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| 02.07.2025, 14:10 (Wednesday) |
TBA |
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| Title: |
TBA
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| Location: |
TBA |
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| Abstract: |
TBA
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