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| 20.10.2021, 14:10 (Wednesday) |
Patrick Iglesias-Zemmour (CNRS, HUJI) |
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| Title: |
Every
symplectic manifold is a (linear) coadjoint orbit |
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| Location: |
Zoom session, the link is available upon request
by email |
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| 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. |
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27.10.2021, 14:10
(Wednesday)
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Daniel Tsodikovich (Tel Aviv University)
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Title:
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Billiard Tables with rotational symmetry |
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| Location: |
Zoom session, the link is available upon request
by email |
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| 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.
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| 03.11.2021, 16:10 (Wednesday) |
Egor Shelukhin (University of Montreal) |
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| (PLEASE NOTE CHANGE IN TIME!)
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| Title: |
Hamiltonian no-torsion |
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| Location: |
Zoom session, the link is available upon request
by email |
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| 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.
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10.11.2021, 14:10 (Wednesday)
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Umut Varolgunes (Stanford University, University
of Edinburgh)
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| Title: |
Trying to quantify Gromov's non-squeezing theorem |
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| Location: |
Zoom session, the link is available upon request
by email |
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| 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. |
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| 17.11.2021, 14:10 (Wednesday) |
Pazit Haim Kislev (Tel Aviv
University) |
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| Title: |
Symplectic capacities of p-products |
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| Location: |
Zoom session, the link is available upon request
by email |
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| 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.
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| 24.11.2021, 14:10 (Wednesday) |
Gerhard Knieper (Ruhr University Bochum) |
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| Title: |
Growth rate of closed geodesics on surfaces
without conjugate points. |
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| Location: |
Zoom session, the link is available upon request
by email |
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| 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. |
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| 01.12.2021, 14:10 (Wednesday) |
Sara Tukachinsky (Tel Aviv University) |
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| Title: |
Bounding chains as a tool in open Gromov-Witten
theory |
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| Location: |
Zoom session, the link is available upon request
by email |
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| 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. |
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| 08.12.2021, 14:10 (Wednesday) |
Louis Ioos (Max Planck Institute) |
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| Title: |
Quantization in stages and canonical metrics |
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| Location: |
Zoom session, the link is available upon request
by email |
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| 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. |
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| 15.12.2021, 14:10 (Wednesday) |
Philippe Charron (Technion)
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| Title: |
Pleijel's theorem for Schrödinger operators |
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| Location: |
Zoom session, the link is available upon request
by email |
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| Abstract: |
We will discuss some recent results regarding the
number of nodal domains
of Laplace and Schrödinger operators. Improving on
Courant's seminal work,
Pleijel's original proof in 1956 was only for domains in
R^2 with Dirichlet
boundary conditions, but it was later generalized to
manifolds (Peetre and
Bérard-Meyer) with Dirichlet boundary conditions, then
to planar domains with
Neumann Boundary conditions (Polterovich, Léna), but
also to the quantum
harmonic oscillator (C.) and to Schrödinger operators
with radial potentials
(C. - Helffer - Hoffmann-Ostenhof). In this recent work
with Corentin Léna,
we proved Pleijel's asymptotic upper bound for a much
larger class of
Schrödinger operators which are not necessarily radial.
In this talk, I will
explain the problems that arise from studying
Schrödinger operators as well
as the successive improvements in the methods that led
to the current results. |
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| 22.12.2021, 14:10 (Wednesday) |
Simion Filip
(University of Chicago) |
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| Title: |
Anosov representations, Hodge theory, and
Lyapunov exponents |
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| Location: |
Zoom session, the link is available upon request
by email |
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| Abstract: |
Discrete subgroups of semisimple Lie groups arise
in a variety of contexts,
sometimes "in nature" as monodromy groups of families of
algebraic manifolds,
and other times in relation to geometric structures and
associated dynamical
systems. I will discuss a class of such discrete
subgroups that arise from
certain variations of Hodge structure and lead to Anosov
representations, thus
relating algebraic and dynamical situations. Among many
consequences of these
relations, I will explain Torelli theorems for certain
families of Calabi-Yau
manifolds (including the mirror quintic), uniformization
results for domains
of discontinuity of the associated discrete groups, and
also a proof of a
conjecture of Eskin, Kontsevich, Moller, and Zorich on
Lyapunov exponents.
The discrete groups of interest live inside the real
linear symplectic group,
and the domains of discontinuity are inside Lagrangian
Grassmanians and other
associated flag manifolds. The necessary context and
background will be explained. |
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| 05.01.2022, 14:10 (Wednesday) |
Igor Uljarević (University of Belgrade) |
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| Title: |
Contact non-squeezing via selective symplectic
homology |
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| Location: |
Zoom session, the link is available upon request
by email |
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| Abstract: |
In this talk, I will introduce a new version of
symplectic homology,
called "selective symplectic homology", that is
associated to a
Liouville domain and an open subset of its boundary. The
selective
symplectic homology is obtained as the direct limit of
Floer homology
groups for Hamiltonians whose slopes tend to infinity on
the open subset
but remain close to 0 and positive on the rest of the
boundary.
I will show how selective symplectic homology can be
used to prove
contact non-squeezing phenomena. One such phenomenon
concerns homotopy
spheres that can be filled by a Weinstein domain with
infinite
dimensional symplectic homology: there exists a
(smoothly) embedded closed
ball in such a sphere that cannot be contactly squeezed
into every
non-empty open subset. As a consequence, there exists a
contact structure
on the standard smooth sphere (in certain dimensions)
that is homotopic to
the standard contact structure but which exhibits
non-trivial contact non-squeezing. |
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| 02.03.2022, 14:10 (Wednesday) |
Joé Brendel (University of Neuchâtel) |
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| Title: |
Squeezing the symplectic ball (up to a subset)
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| Location: |
Zoom session, the link is available upon request
by email |
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| Abstract: |
In a recent preprint, Sackel-Song-Varolgunes-Zhu
investigate quantitative
questions surrounding Gromov's non-squeezing theorem. In
particular, they
show that if one can embed the four-ball into a cylinder
of smaller capacity
after the removal of a subset, then this subset has
Minkowski dimension at
least two. Furthermore, they give an explicit example of
such a "squeezing
up to a subset" where the subset they remove has
dimension two and allows
squeezing by a factor of two (in terms of capacities).
In this talk, we will
discuss certain squeezings by a factor of up to three.
The construction is
inspired by degenerations of the complex projective
plane and almost toric
fibrations. If time permits, we will give a construction
by hand and discuss
how this leads to a different viewpoint on almost toric
fibrations and
potential squeezings in higher dimensions. This is
partially based on work
that will appear as an appendix of the SSVZ paper. |
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| 09.03.2022, 14:10 (Wednesday) |
Jake Solomon (Hebrew University of Jerusalem)
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| Title: |
The cylindrical transform |
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| Location: |
Zoom session, the link is available upon request
by email |
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| Abstract: |
A Lagrangian submanifold of a Calabi-Yau manifold
is called positive if the
restriction to it of the real part of the holomorphic
volume form is positive.
The space of positive Lagrangians admits a Riemannian
metric of non-positive
curvature. Understanding the geodesics of the space of
positive Lagrangian
submanifolds would shed light on questions ranging from
the uniqueness and
existence of volume minimizing Lagrangian submanifolds
to Arnold's nearby
Lagrangian conjecture. The geodesic equation is a
non-linear degenerate elliptic
PDE. I will describe work with A. Yuval on the
cylindrical transform, which
converts the geodesic equation to a family of
non-degenerate elliptic boundary
value problems. As a result, we obtain examples of
geodesics in arbitrary
dimension that are not invariant under any isometries.
The talk will be aimed
at a broad audience. |
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| 16.03.2022, 16:10 (Wednesday) |
Dustin Connery-Grigg (University of Montreal) |
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| (PLEASE NOTE CHANGE IN TIME!)
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| Title: |
Topology of Hamiltonian Floer Complexes in
Dimension 2: Key Ideas and Techniques |
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| Location: |
Zoom session, the link is available upon request
by email |
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| Abstract: |
In general, it is difficult to relate the
structure of the Hamiltonian Floer
complex of a generic pair (H,J) to the dynamical
behaviour of the Hamiltonian
system generated by H. However, it turns out that in
dimension 2, topological
obstructions coming from the braid-theoretic structure
of the periodic orbits
allow us to make significant inroads into understanding
the geometric and dynamical
content of Hamiltonian Floer theory. Some highlights
include a topological
characterization of those Floer chains which represent
the fundamental class
(and which moreover lie in the image of some chain-level
PSS map), as well as
an interpretation of the structure of Floer chain
complexes in homologically
non-trivial degrees in terms of particularly
well-behaved singular foliations
which may be thought of as generalizations of Poincare
sections. In this talk,
I will present the main ideas and techniques which go
into establishing such
results and attempt to sketch some of the main lines of
argument involved in
their proof. |
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| 23.03.2022, 14:10 (Wednesday) |
Pranav Chakravarthy (Hebrew University of
Jerusalem)
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| Title: |
Homotopy type of equivariant symplectomorphisms
of rational ruled surfaces |
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| Location: |
Zoom session, the link is available upon request
by email |
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| Abstract: |
In this talk, we present results on the homotopy
type of the group of
equivariant symplectomorphisms of $S^2 \times S^2$ and
$\mathbb{C}P^2$ blown
up once, under the presence of Hamiltonian group
actions of either $S^1$ or
finite cyclic groups. For Hamiltonian circle
actions, we prove that the
centralizers are homotopy equivalent to either a torus
or to the homotopy
pushout of two tori depending on whether the circle
action extends to a single
toric action or to exactly two non-equivalent toric
actions. We can show that
the same holds for the centralizers of most finite
cyclic groups in the
Hamiltonian group. Our results rely on J-holomorphic
techniques, on Delzant's
classification of toric actions, on Karshon's
classification of Hamiltonian
circle actions on 4-manifolds, and on the
Chen-Wilczy\'nski smooth
classification of $\mathbb{Z}_n$-actions on Hirzebruch
surfaces. |
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| 30.03.2022, 14:10 (Wednesday) |
Maksim Stokic (Tel Aviv University) |
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| Title: |
C^0 contact geometry of isotropic submanifolds |
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| Location: |
Zoom session, the link is available upon request
by email |
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| Abstract: |
The celebrated Eliashberg-Gromov rigidity theorem
states that a diffeomorphism
which is a C^0-limit of symplectomorphisms is itself
symplectic. Contact
version of this rigidity theorem holds true as well.
Motivated by this, contact
homeomorphisms are defined as C^0-limits of
contactomorphisms. Isotropic
submanifolds are a particularly interesting class of
submanifolds, and in this
talk we will try to answer whether or not isotropic
property is preserved by
contact homeomorphisms. Legendrian submanifolds are
isotropic submanifolds of
maximal dimension and we expect that the rigidity holds
in this case. We give
a new proof of the rigidity in dimension 3, and provide
some type of rigidity
in higher dimensions. On the other hand, we show that
the subcritical isotropic
curves are flexible, and we prove quantitative
h-principle for subcritical
isotropic embeddings which is our main tool for proving
the flexibility result. |
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| 06.04.2022, 14:10 (Wednesday) |
Sheng-Fu Chiu (Institute of Mathematics, Academia
Sinica, Taiwan) |
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| Title: |
From Energy-Time Uncertainty to Symplectic
Displacement Energy |
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| Location: |
Zoom session, the link is available upon request
by email |
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| 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. |
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| 27.04.2022, 14:10-15:00 (Wednesday) |
Michael Brandenbursky (Ben-Gurion University) -
TIDY Distinguished Lecture
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| Title: |
C^0-gap between entropy-zero Hamiltonians and
autonomous diffeomorphisms of surfaces |
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| Location: |
Zoom session, the link is available upon request
by email |
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| Abstract: |
Let Σ be a surface equipped with an area form.
There is a long standing open
question by Katok, which, in particular, asks whether
every entropy-zero
Hamiltonian diffeomorphism of a surface lies in the
C^0-closure of the set
of integrable diffeomorphisms. A slightly weaker version
of this question
asks: ``Does every entropy-zero Hamiltonian
diffeomorphism of a surface lie
in the C^0-closure of the set of autonomous
diffeomorphisms?'' In this talk
I will answer in negative the later question. In
particular, I will show that
on a surface Σ the set of autonomous Hamiltonian
diffeomorphisms is not
C^0-dense in the set of entropy-zero Hamiltonians.
Explicitly constructed
examples of such Hamiltonians cannot be approximated by
autonomous
diffeomorphisms. (Joint with M. Khanevsky). |
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| 27.04.2022,
15:10-16:00 (Wednesday) |
Umut
Varolgunes (Bogazici University) - TIDY Distinguished
Lecture
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| Title: |
Computations
in relative symplectic cohomology using local to global
methods |
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| Location: |
Zoom
session, the link is available upon request by email |
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| Abstract: |
Consider a
complete Lagrangian torus fibration p(n) from a
symplectic manifold
to the plane with at most one singular fiber which is a
two torus pinched at
n-meridians. Relative symplectic cohomology in degree 0
defines a sheaf of
algebras in the base with respect to an appropriate
G-topology and grading
datum. I will explain how one can compute this sheaf for
all p(n) using
general properties and explicit computations for p(0).
This is a joint work
with Yoel Groman. |
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A SPECIAL SEMINAR
(PLEASE NOTЕ CHANGE IN TIME AND DATE!)
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| 01.05.2022,
14:00-14:50 (Sunday) |
Egor
Shelukhin (University of Montreal) |
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|
| Title: |
The
transcendental Bézout problem revisited |
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| Location: |
Zoom
session, the link is available upon request by email |
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| Abstract: |
Bézout's
classical theorem states that n complex polynomials of
degree k on C^n
have at most k^n isolated common zeros. The logarithm of
the maximal function
of an entire function on C, instead of the degree,
controls the number of zeros
in a ball of radius r. The transcendental Bézout problem
seeks to extend this
estimate to entire self-mappings f of C^n via the n-th
power of the logarithm
of the maximal function. A celebrated counterexample of
Cornalba-Shiffman shows
that this is dramatically false for n>1. However, it
is true on average, under
lower bounds on the Jacobian, or in a weaker form for
small constant perturbations
of f. We explain how topological considerations of
persistent homology and
Morse theory shed new light on this question proving the
expected bound for a
robust count of zeros. This is part of a larger joint
project with Buhovsky,
Payette, Polterovich, Polterovich, and Stojisavljevic. |
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| 11.05.2022, 14:10 (Wednesday) |
Hyunmoon Kim (Seoul National University) |
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| Title: |
Complex Lagrangian subspaces
and representations of the canonical commutation
relations |
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| Location: |
Zoom session, the link is available upon request
by email |
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| Abstract: |
Complex Lagrangian subspaces were introduced as
polarizations on symplectic
manifolds in geometric quantization. We will look at
their role in the linear
geometry more carefully. A transverse pair of complex
Lagrangian subspaces
parametrizes representations of the canonical
commutation relations and this
brings together some different perspectives from which
the representations
were studied. I will suggest how this result can be
interpreted using concepts
from geometry and very little concepts from physics. |
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| 18.05.2022, 14:10-15:00 (Wednesday) |
Ofir Karin (Tel Aviv University) |
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| Title: |
Approximation of Generating Function Barcode for
Hamiltonian Diffeomorphisms |
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| Location: |
Zoom session, the link is available upon request
by email |
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| Abstract: |
Persistence modules and
barcodes are used in symplectic topology to define
new invariants of Hamiltonian diffeomorphisms, however
methods that explicitly
calculate these barcodes are often unclear. In this talk
I will explain the
necessary background and define one such invariant
called the GF-barcode of
compactly supported Hamiltonian diffeomorphisms of $
\mathbb{R}^{2n} $ by
applying Morse theory to generating functions quadratic
at infinity associated
to such Hamiltonian diffeomorphisms and provide an
algorithm (i.e a finite
sequence of explicit calculation steps) that
approximates it along with a
few computation examples. Joint work with Pazit
Haim-Kislev. |
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|
| 18.05.2022,
15:10-16:00
(Wednesday) |
Alexey
Balitskiy (IAS Princeton, and Institute for Information
Transmission Problems RAS) |
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| Title: |
Systolic
freedom and rigidity modulo 2 |
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| Location: |
Zoom
session, the link is available upon request by email |
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| Abstract: |
The
$k$-dimensional systole of a closed Riemannian
$n$-dimensional manifold $M$
is the infimal $k$-volume of a non-trivial $k$-cycle
(with some coefficients).
In '90s, Gromov asked if the product of the $k$-systole
and the $(n-k)$-systole
is bounded from above by the volume of $M$ (up to a
dimensional factor); this
would manifest the \emph{systolic rigidity}. Freedman
exhibited the first
examples with $k=1$ and mod 2 coefficients where this
fails; this manifests
the \emph{systolic freedom}. In a joint work in progress
with Hannah Alpert
and Larry Guth, we show that Freedman's examples are
almost as "free" as
possible, and the systolic rigidity almost holds, with
$k=1$ and mod 2
coefficients. Namely, on a manifold of bounded local
geometry,
$\mbox{systole}_1(M) \cdot \mbox{systole}_{n-1}(M) \le
c_\epsilon \mbox{volume}(M)^{1+\epsilon}$,
as long as the left-hand side is finite ($H_1(M;
\mathbb{Z}/2)$ is non-trivial).
The proof, which I will explain, is based on the
Schoen--Yau--Guth--Papasoglu
minimal surface method.
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| 25.05.2022, 14:10 (Wednesday) |
Alexander A. Trost (Ruhr University Bochum)
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| Title: |
Elementary bounded generation for global function
fields and some applications |
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| Location: |
Zoom session, the link is available upon request
by email |
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| Abstract: |
Bounded generation (and elementary bounded
generation) are essentially the
ability to write each element of a given group as
products with factors from
a finite collection of ”simple” subgroups of the group
in question and with
a uniform bound on the number of factors needed. These
somewhat technical
properties were initially introduced in the study of the
congruence subgroup
property of arithmetic groups, but they traditionally
also found applications
in the representation theory of these groups, their
subgroup growth and
Kazdhan’s Property (T). Recently however, there has been
renewed interest in
these properties from the area of geometric group theory
as bounded elementary
generation appears naturally as a technical assumption
in various results
studying arithmetic groups ranging from the study of
conjugation-invariant
norms on, say, SLn as well as in the study of the
first-order theories of
arithmetic groups. Classical results in this area were
usually concerned with
groups arising from number fields though and somewhat
surprisingly there are
few such results for groups arising from global function
fields. In this talk,
I will give a short introduction about the history of
bounded generation in
general and then present a general bounded generation
for split Chevalley
groups arising from global function fields together with
some applications
if time allows.
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| 01.06.2022, 14:10 (Wednesday) |
Matthias Meiwes (RWTH Aachen University) |
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| Title: |
Entropy, braids, and Hofer's metric |
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| Location: |
Zoom session, the link is available upon request
by email |
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| Abstract: |
Topological entropy captures the orbit complexity
of a dynamical system with
the help of a single non-negative number. Detecting
robustness of this number
under perturbation is a way to understand stability
features of a chaotic system.
In my talk, I will address the problem of robustness of
entropy for Hamiltonian
diffeomorphisms in terms of Hofer's metric. Our main
focus lies on dimension 2,
where there is a strong connection between topological
entropy and the existence
of specific braid types of periodic orbits. I explain
that the construction of
eggbeater maps of Polterovich-Shelukhin and their
generalizations by Chor provide
robustness even under large perturbation: the entropy
will not drop much when
perturbing the specific diffeomorphism in some ball of
large Hofer-radius.
I furthermore discuss a result that any braid of
non-degenerate one-periodic
orbits with pairwise homotopic strands persists under
generic Hofer-small
perturbations, which yields a local entropy robustness
result for surfaces.
This talk is based on joint works with Arnon Chor, and
Marcelo Alves. |
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| 08.06.2022, 14:10 (Wednesday) |
David Miyamoto (University of Toronto) |
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| Title: |
Quasifold groupoids and
diffeological quasifolds |
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| Location: |
Zoom session, the link is available upon request
by email |
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| Abstract: |
A quasifold is a space that is locally modeled by
quotients of R^n
by countable group actions. These arise in Elisa Prato's
generalization of
the Delzant theorem to irrational polytopes, and include
orbifolds and
manifolds. We approach quasifolds in two ways: by
viewing them as diffeological
spaces, we form the category of diffeological
quasifolds, and by viewing them
as Lie groupoids (with bibundles as morphisms), we form
the category of
quasifold groupoids. We show that, restricting to
effective groupoids, and
locally invertible morphisms, these two categories are
equivalent. In
particular, an effective quasifold groupoid is
determined by its diffeological
orbit space. This is join work with Yael Karshon. |
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A SPECIAL ANNOUNCEMENT:
TIDY DISTINGUISHED LECTURES
BY PROF. MARK LEVI |
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| 13.06.2022,
14:00 (Monday) |
Mark Levi
(Penn State) -
TIDY Distinguished Lecture |
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| Title: |
Counterintuitive
effects in mechanics |
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| Location: |
Schreiber
bldg., room 6, Tel Aviv University
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| Abstract: |
Two of the
best known counterintuitive effects in mechanics are the
stability
of the spinning top and the stability of the upside-down
pendulum with the
pivot subjected to rapid vertical vibrations -- the
so-called Kaptisa effect
(discovered in 1908 by Stephenson when Kapitsa was about
14).
To this list can be added a much less known recently
discovered mechanical
analog of Faraday’s law, the so-called ponderomotive
Lorentz force: a rapidly
changing force field gives rise to a magnetic-like
effect: for example, a
particle of dust in the gravitational field of a rapidly
rotating elongated
asteroid acts as if it were electrically charged and in
some magnetic field.
That is, the averaged motion of the mechanical particle
is identical to the
motion of a fictitious electrically charged particle in
a fictitious magnetic
field. I will describe this result, as well as some
observations that came
out of attempts at a geometrical explanation of the
ponderomotive Lorentz
force. One of these observations is the role of Gaussian
curvature in the
dynamics of the Lagrange top. This talk is based on
joint work with Graham Cox. |
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| 15.06.2022,
14:00 (Wednesday) |
Mark Levi
(Penn State) -
TIDY Distinguished Lecture |
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| Title: |
Sharp
Arnold tongues and fragile Frenkel-Kontorova equilibria |
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| Location: |
Schreiber
bldg., room 6, Tel Aviv University |
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| Abstract: |
J. B.
Keller and D. Levy discovered an interesting effect: the
instability
tongues in Mathieu-type equations become duller with the
addition of higher
harmonics in the Mathieu potentials. 20 years
later V. Arnold rediscovered
this effect, and also found a similarly flavored
phenomenon in circle maps:
namely, the fewer harmonics in the perturbation of the
pure rotation, the
sharper are the Arnold tongues. Incidentally, the proofs
of the two effects
are entirely different, despite the similarity of
flavors. I will describe
another result of similar kind for area-preserving
non-exact cylinder maps.
The observation was motivated by the study of traveling
waves in the discretized
sine-Gordon equation/coupled pendula, and by the study
of the Frenkel-Kontorova
equilibria. I will describe these results, including one
on the surprising
fragility of equilibria of the Frenkel-Kontorova model.
This talk is based on
joint work with Jing Zhou. |
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A SPECIAL ANNOUNCEMENT:
VI International Conference
on
Finite Dimensional
Integrable Systems in Geometry and Mathematical
Physics
June 20-24, 2022, Tel
Aviv University
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