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| 26.10.2022, 14:10 (Wednesday) |
Cheuk Yu Mak (University of Edinburgh) |
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| Title: |
Some cute
applications of Lagrangian cobordisms |
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| Location: |
Zoom session |
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| Abstract: |
In this
talk, we will discuss, from a quantitative aspect, the
following
symplectic questions: packing Lagrangian submanifolds,
displacing Lagrangian
submanifolds, and constructing Lagrangian surfaces with
a prescribed genus.
We will illustrate some interesting features of these
questions using simple
examples. The focus will be put on explaining some new
ideas from the point
of view of Lagrangian cobordisms. This is a joint work
with Jeff Hicks. |
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02.11.2022, 17:10
(Wednesday)
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Pierre-Alexandre Mailhot (University of Montreal)
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| (PLEASE NOTE CHANGE IN TIME!)
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Title:
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Spectral diameter, Liouville domains and
symplectic cohomology |
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| Location: |
Zoom session |
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| Abstract: |
The spectral norm provides a lower bound to the
Hofer norm. It is thus
natural to ask whether the diameter of the spectral norm
is finite or not.
In the case of closed symplectic manifolds, there is no
unified answer.
For instance, for a certain class of symplecticaly
aspherical manifolds,
which contains surfaces, the spectral diameter is
infinite. However, for
CP^n, the spectral diameter is known to be finite.
During this talk, I will
prove that, in the case of Liouville domains, the
spectral diameter is
finite if and only if the symplectic cohomology of the
underlying manifold
vanishes. With that relationship in hand, we will
explore applications to
symplecticaly aspherical symplectic manifolds and give a
new proof that the
spectral diameter is infinite on cotangent disk bundles.
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| 09.11.2022, 14:10 (Wednesday) |
Grigory Mikhalkin (University of Geneva) -
Blumenthal Lecture in Geometry |
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| Title: |
Toric geometry and tropical trigonometry |
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| Location: |
Schreiber bldg., room 309, Tel Aviv University
(and online via zoom)
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| Abstract: |
Toric varieties were constructed as algebraic
varieties about 50 years ago,
and also as symplectic varieties about 40 years ago. The
two constructions
are dual to each other, but are based on the same
geometry in R^n. Symmetries
in this geometry are linear transformations given by
invertible n-by-n
matrices with integer coefficients, as well as all
translations. This makes
the notion of a tangent integer vector as well as a
notion of tropical curve
well-defined. The talk will review basic constructions
with a focus on
tropical triangles that underlie some recent progress in
symplectic embedding
problems.
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SPECIAL ANNOUNCEMENT -
SEMINAR IN REAL AND COMPLEX GEOMETRY
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| 10.11.2022,
16:15 (Thursday) |
Grigory
Mikhalkin (University of Geneva) - Blumenthal Lecture in
Geometry |
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| Title: |
Tropical,
real and symplectic geometry |
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| Location: |
Orenstein bldg., room 111, Tel Aviv
University (and online via zoom)
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| Abstract: |
This
lecture will focus on the way how tropical curves appear
in symplectic
geometry settings. On one hand, tropical curves can be
lifted as Lagrangian
submanifolds in the ambient toric variety. On the other
hand, they can be
lifted as holomorphic curves. The two lifts use two
different tropical
structures on the same space, related by a certain
potential function. We
pay special attention to correspondence theorems between
tropical curves and
real curves, i.e. holomorphic curves invariant with
respect to an
antiholomorphic involution. The resulting real curves
produce, in their
turn, holomorphic membranes for tropical Lagrangian
submanifolds. |
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16.11.2022, 14:10 (Wednesday)
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Jinxin Xue (Tsinghua University) |
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| Title: |
Dynamics of composite symplectic Dehn twists |
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| Location: |
Zoom session (and screening in Schreiber bldg.,
room 309, Tel Aviv University) |
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| Abstract: |
It is classically known in Nielson-Thurston
theory that the mapping class
group of a hyperbolic surface is generated by Dehn
twists and most elements
are pseudo Anosov. Pseudo Anosov elements are
interesting dynamical objects.
They are featured by positive topological entropy and
two invariant singular
foliations expanded or contracted by the dynamics. We
explore a generalization
of these ideas to symplectic mapping class groups. With
the symplectic Dehn
twists along Lagrangian spheres introduced by Arnold and
Seidel, we show in
various settings that the compositions of such
twists has features of pseudo
Anosov elements, such as positive topological entropy,
invariant stable and
unstable laminitions, exponential growth of Floer
homology group, etc. This
is a joint work with Wenmin Gong and Zhijing Wang. |
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| 23.11.2022, 17:10 (Wednesday) |
Marcelo S. Atallah
(University of Montreal) |
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| (PLEASE NOTE CHANGE IN TIME!)
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| Title: |
Fixed points of small Hamiltonian diffeomorphisms
and the Flux conjectures |
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| Location: |
Zoom session |
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| Abstract: |
Inspired by the work of
Lalonde-McDuff-Polterovich, we describe how the C^0
and C^1 flux conjectures relate to new instances of the
strong Arnol’d
conjecture and make new progress on the C0 flux
conjecture. This is joint
work in progress with Egor Shelukhin.
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| 30.11.2022, 14:10 (Wednesday) |
Joé Brendel (Tel Aviv University) |
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| Title: |
Pinwheels as Lagrangian barriers |
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| Location: |
Schreiber bldg., room 309, Tel Aviv University
(and online via zoom) |
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| Abstract: |
Pinwheels are certain singular Lagrangians in
four-dimensional
symplectic manifolds. In this talk we focus on the case
of the complex
projective plane, where pinwheels arise naturally as
visible Lagrangians
in its almost toric fibrations or, alternatively, as
vanishing cycles of
its degenerations. Pinwheels have been shown to have
interesting
rigidity properties by Evans--Smith. The goal of this
talk is to show
that Lagrangian pinwheels are Lagrangian barriers in the
sense of Biran,
meaning that their complement has strictly smaller
Gromov width than the
ambient space. Furthermore, we will discuss a connection
to the Lagrange
spectrum. This is joint work with Felix Schlenk. |
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| 07.12.2022, 14:10 (Wednesday) |
Yoel Groman (Hebrew University of Jerusalem) |
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| Title: |
Closed string mirrors of symplectic cluster
manifolds |
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| Location: |
Schreiber bldg., room 309, Tel Aviv University
(and online via zoom) |
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| Abstract: |
Consider a symplectic Calabi Yau manifold
equipped with a Maslow 0 Lagrangian
torus fibration with singularities. According to modern
interpretations of
the SYZ conjecture, there should be an associated
analytic mirror variety
with a non Archimedean torus fibration over the same
base. I will suggest a
general construction called the closed string mirror
which is based on
relative symplectic cohomologies of the fibers. A priori
the closed string
mirror is only a set with a map to the base, but
conjecturally under some
general hypotheses it is in fact an analytic variety
with its non Archimedean
torus fibration. I will discuss joint work with Umut
Varolgunes where we prove
this in the case of four dimensional symplectic cluster
manifolds. |
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| 14.12.2022, 14:10 (Wednesday) |
Mira Shamis (Queen Mary University of London) |
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| Title: |
On the abominable properties of the Almost
Mathieu operator with Liouville frequencies |
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| Location: |
Schreiber bldg., room 309, Tel Aviv University
(and online via zoom) |
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| Abstract: |
We show that, for
sufficiently well approximable frequencies, several
spectral characteristics of the Almost Mathieu operator
can be as poor
as at all possible in the class of all discrete
Schroedinger
operators. For example, the modulus of continuity of the
integrated
density of states may be no better than logarithmic.
Other
characteristics to be discussed are homogeneity, the
Parreau-Widom
property, and (for the critical AMO) the Hausdorff
content of the
spectrum. Based on joint work with A. Avila, Y. Last,
and Q. Zhou.
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| 21.12.2022, 14:10 (Wednesday) |
Maksim Stokic (Tel Aviv University)
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| Title: |
Flexibility of the adjoint action of the group of
Hamiltonian diffeomorphisms |
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| Location: |
Schreiber bldg., room 309, Tel Aviv University
(and online via zoom) |
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| Abstract: |
The space of Hamiltonian diffeomorphisms has a
structure of an infinite
dimensional Frechet Lie group, with Lie algebra
isomorphic to the space
of normalized functions and adjoint action given by
pull-backs. We show
that this action is flexible: for a non-zero normalized
function $f$,
any other normalized function can be written as a sum of
differences of
elements in the orbit of $f$ generated by the adjoint
action. Additionally,
the number of elements in this sum is dominated from
above by the
$L_{\infty}$-norm of $f$. This result can be interpreted
as an (bounded)
infinitesimal version of the Banyaga's result on
simplicity of $Ham(M,\omega)$.
Moreover, it can be used to remove the
$C^{\infty}$-continuity condition
in the Buhovsky-Ostrover theorem on the uniqueness of
Hofer's metric.
This is joint work with Lev Buhovsky. |
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| 28.12.2022, 14:10 (Wednesday) |
Albert Fathi
(Georgia Tech) |
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| Title: |
Smooth Lyapunov functions on closed subsets and
isolating neighbourhoods |
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| Location: |
Schreiber bldg., room 309, Tel Aviv University
(and online via zoom) |
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| Abstract: |
We will discuss unified and simplified proofs of
some previously known
theorems relating dynamics and Lyapunov functions. In
particular, we
will give a proof of the existence of isolating blocks
for isolated
invariant sets. |
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| 04.01.2023, 14:00-15:00 (Wednesday) |
Iosif Polterovich (University of Montreal)
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| (PLEASE NOTE CHANGE IN TIME!)
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| Title: |
Pólya's eigenvalue conjecture: some recent
advances |
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| Location: |
Schreiber bldg., room 309, Tel Aviv University
(and online via zoom) |
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| Abstract: |
The celebrated Pólya’s conjecture (1954) in
spectral geometry states that
the eigenvalue counting functions of the Dirichlet and
Neumann Laplacian
on a bounded Euclidean domain can be estimated from
above and below,
respectively, by the leading term of Weyl’s asymptotics.
The conjecture
is known to be true for domains which tile the Euclidean
space, however
it remains largely open in full generality. In the talk
we will explain
the motivation behind this conjecture and discuss some
recent advances,
notably, the proof of Pólya’s conjecture for the disk.
The talk is based
on a joint work with Nikolay Filonov, Michael Levitin
and David Sher. |
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| 04.01.2023,
15:20-16:20 (Wednesday) |
Shira Tanny
(IAS Princeton) |
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| (PLEASE NOTE CHANGE IN TIME AND LOCATION!) |
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| Title: |
Closing
lemmas in contact dynamics and holomorphic curves |
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| Location: |
Schreiber
bldg., room 209, Tel Aviv University (and online via
zoom) |
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| Abstract: |
Given a
flow on a manifold, how to perturb it in order to create
a periodic
orbit passing through a given region? While the first
results in this
direction were obtained in the 1960-ies, various facets
of this question
remain largely open. I will review recent advances on
this problem in the
context of contact flows, which are closely related to
Hamiltonian flows
from classical mechanics. In particular, I'll discuss a
proof of a
conjecture of Irie stating that rotations of
odd-dimensional ellipsoids
admit a surprisingly large class of perturbations
creating periodic orbits.
The proof involves methods of modern symplectic topology
including
pseudo-holomorphic curves and contact homology. The talk
is based on a
joint work with Julian Chaidez, Ipsita Datta and Rohil
Prasad, as well
as a work in progress joint with Julian Chaidez. |
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| 11.01.2023, 17:10 (Wednesday) |
Yuhan Sun (Rutgers University) |
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| (PLEASE NOTE CHANGE IN TIME!)
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| Title: |
Heavy sets and relative symplectic cohomology
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| Location: |
Zoom session |
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| Abstract: |
Heavy sets were introduced by Entov-Polterovich
around 2009. They reveal
suprising rigidity of certain compact subsets of a
closed symplectic manifold,
from a functional persepective. When a compact subset is
a smooth Lagrangian
submanifold, there is a well-established relation
between its heaviness and
the non-vanishing of its Lagrangian Floer cohomology. In
this talk we
describe an equivalence between the heaviness of general
compact subsets
and the non-vanishing of another Floer-type invariant,
called the relative
symplectic cohomology. If time permits, we will discuss
applications and
questions we learned from this equivalence. Based on
joint work with C.Mak
and U.Varolgunes.
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18.01.2023, 14:10 (Wednesday)
|
Michael Entov (Technion) |
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| Title: |
Kahler-type embeddings of balls into symplectic
manifolds |
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| Location: |
Schreiber bldg., room 309, Tel Aviv University
(and online via zoom) |
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| Abstract: |
A symplectic embedding of a disjoint union of
balls into a symplectic
manifold M is called Kahler-type if it is holomorphic
with respect
to some (not a priori fixed) complex structure on M
compatible with
the symplectic form. Assume that M either of the
following: CP^n (with
the standard symplectic form), an even-dimensional torus
or a K3 surface
equipped with an irrational Kahler-type symplectic form.
Then:
1. Any two Kahler-type embeddings of a disjoint union of
balls into M
can be mapped into each other by a symplectomorphism
acting trivially on
the homology. If the embeddings are holomorphic with
respect to complex
structures compatible with the symplectic form and lying
in the same
connected component of the space of Kahler-type complex
structures on M,
then the symplectomorphism can be chosen to be smoothly
isotopic to the
identity.
2. Symplectic volume is the only obstruction for the
existence of
Kahler-type embeddings of k^n equal balls (for any k)
into CP^n and of
any number of possibly different balls into a torus or a
K3 surface.
This is a joint work with M.Verbitsky. |
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| 15.03.2023, 14:10 (Wednesday) |
Ely Kerman (University of Illinois
Urbana-Champaign) |
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| Title: |
Mean width, symplectic capacities and volume
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| Location: |
Schreiber bldg., room 309, Tel Aviv University
(and online via zoom) |
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| Abstract: |
In this talk, I will discuss an inequality
between a symplectic version
of the mean width of a convex body and its symplectic
capacity. This is
motivated by and generalizes an equality established by
Artstein-Avidan
and Ostrover. The proof utilizes their symplectic
Brunn-Minkowski
inequality together with a local version of Viterbo's
conjecture
established by Abbondandolo and Benedetti. I will also
describe several
examples and secondary results that suggest that the
difference between
the symplectic mean width and the mean width is deeply
related to toric
symmetry. This is joint work in progress with Jonghyeon
Ahn. |
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| 22.03.2023, 14:10 (Wednesday) |
Laurent Charles (Sorbonne University, Paris)
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| Title: |
On magnetic Laplacian on compact surfaces |
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| Location: |
Schreiber bldg., room 309, Tel Aviv University
(and online via zoom) |
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| Abstract: |
I will discuss the relations between magnetic
geodesic flows
on closed manifolds and the corresponding quantum
Hamiltonians. For
hyperbolic surfaces with constant magnetic field, the
magnetic flow is
periodic up to some critical energy, and the
corresponding eigenvalues
of the magnetic Laplacian have high degeneracies.
More generally, in the semiclassical limit,
magnetic Laplacians have
spectral clusters. In each cluster, the dynamic and the
eigenvalue
distribution can be described in terms of Toeplitz
operators.
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| 29.03.2023, 14:10 (Wednesday) |
Pazit Haim-Kislev (Tel Aviv University) |
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| Title: |
Symplectic Barriers |
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| Location: |
Schreiber bldg., room 309, Tel Aviv University
(and online via zoom) |
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| Abstract: |
In his seminal 2001 paper, Biran introduced the
concept of Lagrangian
Barriers, a symplectic rigidity phenomenon
coming from obligatory
intersections with Lagrangian submanifolds which doesn't
come from
mere topology. Since then several other examples for
Lagrangian barriers
have been discovered. In this joint work with Richard
Hind and Yaron
Ostrover, we introduce the first example (as far as we
know) of Symplectic
Barriers, a symplectic rigidity coming from
obligatory intersections of
symplectic embeddings with symplectic submanifolds (and
in particular
not Lagrangian). |
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Special seminar:
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| 18.04.2023,
16:10 (Tuesday) |
River
Chiang (National Cheng Kung University) |
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| Title: |
Examples of
higher dimensional non-fillable contact manifolds |
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| Location: |
Kaplun
bldg., room 205, Tel Aviv University |
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|
| Special seminar: |
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| 19.04.2023,
11:00 (Wednesday) |
Boris
Khesin (University of Toronto) |
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| Title: |
Geodesic
framework for vortex sheets and generalized fluid flows |
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| Location: |
Schreiber
bldg., room 309, Tel Aviv University |
|
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| Abstract: |
We discuss
ramifications of Arnold’s group-theoretic approach to
ideal
hydrodynamics as the geodesic flow for a right-invariant
metric on the
group of volume-preserving diffeomorphisms. It turns out
that many
equations of mathematical physics, such as the motion of
vortex sheets
or fluids with moving boundary, have Lie groupoid,
rather than Lie
group, symmetries.
We present their geodesic setting, which also allows one
to describe
multiphase fluids, homogenized vortex sheets and
Brenier’s generalized flows.
This is a joint work with Anton Izosimov. |
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| 19.04.2023, 14:10-15:00 (Wednesday) |
Viktor L. Ginzburg (University of California,
Santa Cruz) - TIDY Distinguished Lecture
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| Title: |
Topological Entropy of Reeb Flows, Barcodes and
Floer Theory |
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| Location: |
Schreiber bldg., room 309, Tel Aviv University
(and online via zoom) |
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| Abstract: |
Topological entropy is one of the fundamental
invariants of a dynamical
system, measuring its complexity. In this talk, we focus
on connections
between the topological entropy of a Hamiltonian
dynamical system, e.g.,
a Hamiltonian diffeomorphism or a Reeb or geodesic flow,
and its
Symplectic/Floer homology. We recall the definition of
barcode entropy —
a Floer theoretic counterpart of topological entropy —
and discuss
possible ways to extend it to Reeb flows. The talk is
based on joint
work with Erman Cineli, Basak Gurel and Marco
Mazzucchelli. |
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| 19.04.2023,
15:10-16:00 (Wednesday) |
Başak Z.
Gürel (University of Central Florida) - TIDY
Distinguished Lecture
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| Title: |
On the
volume of Lagrangian submanifolds |
|
| Location: |
Schreiber
bldg., room 309, Tel Aviv University (and online via
zoom) |
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| Abstract: |
We will
discuss the continuity property of the surface area of
Lagrangian
submanifolds, or to be more precise its lower
semi-continuity with respect
to the gamma-norm, and connections with integral
geometry, Floer theory
and barcodes. The talk is based on joint work with Erman
Cineli and
Viktor Ginzburg. |
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Special joint G&D and RCG seminar:
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| 27.04.2023,
16:15 (Thursday) |
Igor
Zelenko (Texas A&M University) |
|
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|
| Title: |
Gromov's
h-principle for corank two distribution of odd rank with
maximal first Kronecker index |
|
| Location: |
Schreiber
bldg., room 309, Tel Aviv University (and online via
zoom) |
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| Abstract: |
Many
natural geometric structures on manifolds are given as
sections of
certain bundles satisfying open relations at every
point, depending on
the derivatives of these sections. Such relations are
called open
differential relations. Symplectic, contact, and even
contact structures
on manifolds can be described in this way. The natural
question is: do
structures satisfying given open relations (called the
genuine solutions
of the differential relation) exist on a given manifold?
Replacing all
derivatives appearing in a differential relation by the
additional
independent variables, one obtains an open subset of the
corresponding
jet bundle. A formal solution of the differential
relation is a section
of the jet bundle lying in this open set. The existence
of a formal
solution is obviously a necessary condition for the
existence of the
genuine one. One says that a differential relation
satisfies a
(nonparametric) h-principle if any formal solution is
homotopic to
the genuine solution in the space of formal solutions.
Versions of the h-principle have been successfully
established for
corank 1 distributions satisfying natural open
relations. Such results
are among the most remarkable advances in
differential topology in the
last four decades. However, very little is known about
analogous results
for other classes of distributions, e.g. generic
distributions of corank 2
or higher (except the so-called Engel distributions, the
smallest
dimensional case of maximally nonholonomic
distributions of corank 2
distributions on 4-dimensional manifolds).
In my talk, I will show how to use the method of convex
integration in
order to establish all versions of the h-principle for
corank 2
distributions of arbitrary odd rank satisfying a natural
generic
assumption on the associated pencil of skew-symmetric
forms. During
the talk, I will try to give all the necessary
background. This is the
joint work with Milan Jovanovic, Javier
Martinez-Aguinaga, and
Alvaro del Pino. |
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SPECIAL ANNOUNCEMENT -
TAU Math Colloquium:
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|
| 01.05.2023,
12:15 (Monday) |
Shmuel
Weinberger (University of Chicago) - TIDY Distinguished Lecture
1/2
|
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|
|
| Title: |
Finite
group actions on aspherical spaces |
|
| Location: |
Schreiber
bldg., room 006, Tel Aviv University |
|
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|
| Abstract: |
I will
start by explaining why any finite simplicial
complex is the fixed set of a simplicial action of a
group of order
120 on some high dimensional disk. (This is based on
work from the
1970s of Jones, Oliver, Assadi and others). The
analogous question
for the product of a circle and a disk is much more
difficult. I will
discuss this latter problem (following joint work with
Cappell and
Yan) and try to explain how traces in algebraic K-theory
(no knowledge
of this topic assumed) enter in this and a much wider
class of
problems.
This is the first talk of the 2023 TIDY lecture series
titled
Some geometry associated to torsion in discrete
groups. |
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|
| 03.05.2023, 14:10 (Wednesday) |
Shmuel Weinberger (University of Chicago) - TIDY Distinguished Lecture
2/2
|
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|
|
| Title: |
Torsion, L^2 cohomology and complexity |
|
| Location: |
Schreiber bldg., room 309, Tel Aviv University
(and online via zoom) |
|
|
|
|
| Abstract: |
This talk is a hermitian analog of the previous
one, but is
completely independent of it in terms of its actual
content.
Atiyah introduced real valued L^2 betti numbers as a way
of
understanding the (usually infinite dimensional)
cohomology of
universal covers of finite complexes. As far as
anyone knows these
are always integers for torsion free fundamental group,
but for groups
with torsion very much more exotic possibilities arise.
We will use this and an invariant of Cheeger and Gromov
to see that
whenever an oriented smooth manifold of dimension 4k+3
has torsion in
its fundamental group, there are many other manifolds
homotopy
equivalent but not diffeomorphic to it and that in the
known
situations where betti numbers can be irrational there
is even an
infinitely generated group of such! And, I will
also use this
invariant to explain how many simplices (roughly) it
takes to build a
standard Lens space. This is based on old work
with Stanley Chang,
and recent work with Geunho Lim.
This is the second
talk of the 2023 TIDY lecture series titled
Some geometry associated to torsion in discrete
groups. |
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| 10.05.2023, 14:10-15:00 (Wednesday) |
Gleb Smirnov (University of Geneva) |
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| Title: |
Lagrangian rigidity in K3 surfaces |
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| Location: |
Zoom session (and screening in Schreiber bldg.,
room 309, Tel Aviv University) |
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| Abstract: |
Sheridan-Smith and Entov-Verbitsky show that
every Maslov-zero Lagrangian
torus in a K3 surface has a nontrivial and primitive
homology class.
In this talk, we prove the "nontrivial" part of their
theorem with a
different method and the converse result. |
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| 10.05.2023,
15:10-16:00 (Wednesday) |
Marcelo R.
R. Alves (University of Antwerp) |
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| Title: |
C^0-stability
of topological entropy for 3-dimensional Reeb flows |
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| Location: |
Schreiber
bldg., room 309, Tel Aviv University (and online via
zoom) |
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| Abstract: |
The
C^0-distance on the space of contact forms on a contact
manifold has
been studied recently by different authors. It can be
thought of as an
analogue for Reeb flows of the Hofer metric on the space
of Hamiltonian
diffeomorphisms. In this talk, I will explain some
recent progress on
the stability properties of the topological entropy with
respect to this
distance. This is joint work with Lucas Dahinden,
Matthias Meiwes and
Abror Pirnapasov. |
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| 17.05.2023, 14:10 (Wednesday) |
Joé Brendel (Tel Aviv University) |
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| Title: |
Lagrangian product tori in $S^2 \times S^2$ |
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| Location: |
Schreiber bldg., room 309, Tel Aviv University
(and online via zoom) |
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| Abstract: |
A Lagrangian product torus in $S^2 \times S^2$ is
a Lagrangian
torus obtained by taking a product of circles. The main
goal of this
talk is to give a symplectic classification of product
tori and
illustrate that interesting things can happen in case
the symplectic
form is non-monotone. We make a detour through toric
geometry and
discuss the more general classification question of
toric fibres. If
time permits, we will discuss related questions and some
applications.
This is partially based on joint work with Joontae Kim. |
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| 24.05.2023,
14:10 (Wednesday) |
Ilia Gaiur
(University of Toronto, Weizmann Institute of Science) |
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| Title: |
Normal
forms in the truncated gl_n Lie algebras |
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| Location: |
Schreiber
bldg., room 309, Tel Aviv University |
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| Abstract: |
Fix a
finite dimensional Lie algebra $\mathfrak{g}$. The
truncated loop
algebra of $\mathfrak{g}$ is a finite dimensional Lie
algebra which
may be seen as the algebra of r-jets of maps from
$\mathbb{C}^*$ to
$\mathfrak{g}$. Such algebras are examples of finite
dimensional
non-semisimple Lie algebras which, however, allow a nice
description.
I will give a review of the Lie-Poisson theory for such
algebras and
will explain in detail the geometry of the co-adjoint
orbits of such
algebras corresponding to $\mathfrak{gl}_n$. I will
introduce the
notion of a normal form for such Lie algebras and
discuss degenerations
of their co-adjoint orbits. At the end of the talk I
will give a brief
review of how different types of geometries appear in
the study of
integrable systems and moduli spaces of differential
equations. |
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| 31.05.2023, 14:10 (Wednesday) |
Lenya Ryzhik (Nirit and Michael Shaoul Fellow,
Stanford University) |
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| Title: |
Diffusion of learning models |
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| Location: |
Schreiber bldg., room 309, Tel Aviv University
(and online via zoom) |
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| Abstract: |
The notion of diffusion of
knowledge goes at least as far back to
Chapter 1 of the "Pickwick Papers". However, its
mathematical modeling
in macroeconomics is much more recent. We will discuss
some models
proposed by R. Lucas and B. Moll about ten years ago.
Various versions lead to the mean field games type PDE
and also
infinite-dimensional optimal control Hamilton-Jacobi
problems. We will
discuss the little mathematical progress but mostly
focus on the
modeling and open questions aspects. |
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| 07.06.2023, 14:10 (Wednesday) |
Hyunmoon
Kim (University of Toronto, Tel Aviv University) |
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| Title: |
The real orbits of complex Lagrangian
Grassmannians |
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| Location: |
Schreiber bldg., room 309, Tel Aviv University
(and online via zoom) |
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| Abstract: |
The Riemann sphere can be broken up into three
orbits of SL(2, R), as
two open hemispheres and a great circle. We will discuss
a generalization
of this phenomenon in complex Lagrangian Grassmannians
of higher
dimensions under the action of the real symplectic
group. We will
give formulas for the number of orbits, incidence
relations, and
their dimensions. We will also show homotopy
equivalences between
these orbits and some other Grassmannian objects, and if
time permits,
a strategy to compute their homology. |
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| 14.06.2023, 14:10 (Wednesday) |
Lev Birbrair (The Federal University of Ceará and
Jagiellonian University) |
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| Title: |
Outer Lipschitz Geometry of germs of
Semialgebraic (Definable) surfaces |
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| Location: |
Zoom session (and screening in Schreiber bldg.,
room 309, Tel Aviv University) |
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| Abstract: |
I am going to describe the first attempt of outer
Lipschitz Classification
of germs of Semialgebraic Surfaces. We show how the
classification
question can be solved for a special case - the
surfaces, obtained as
a union of two Normally Embedded Hölder triangles. |
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| 21.06.2023, 14:10 (Wednesday) |
Stefan Nemirovski (Steklov Mathematical Institute
and Ruhr University Bochum) |
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| Title: |
Legendrian links and déjà vu
moments |
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| Location: |
Zoom session (and screening in Schreiber bldg.,
room 309, Tel Aviv University) |
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| Abstract: |
Legendrian links in the space of null geodesics
of a spacetime
can be used to detect "déjà vu moments", i.e. different
instances
at which an observer receives the same light ray. In the
talk,
I'll discuss the relevant class of Legendrian links and
some
ensuing open problems. |
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