

08.11.2023, 14:10 (Wednesday)

PierreAlexandre Arlove (Ruhr University Bochum) 




Title: 
Contact orderability and spectral selectors 

Location: 
Zoom session 




Abstract: 
Some contactomorphisms groups and isotopy classes
of
Legendrians admit a natural partial order first studied
by Eliashberg
and Polterovich. In this talk I will use this partial
order to define
functions on the latter spaces analogous to the spectral
invariants in
Symplectic Geometry coming from Lagrangian Floer
homology. For
Legendrians, I will show that these functions are
spectral selectors
and, from there, derive dynamical applications such as
the existence of
translated points and interlinked Legendrians. After
discussing the
nondegeneracy of the selectors, I will present
applications to the
geometric study of these spaces, namely : construction
of timefunctions
and the study of various metrics. This is a joint work
with Simon
Allais. 









15.11.2023, 14:10 (Wednesday) 
Dan Mangoubi (Hebrew
University) 




Title: 
On the inner radius of nodal domains 

Location: 
Zoom session 




Abstract: 
By the well known FaberKrahn
inequality the first Dirichlet Laplace
eigenvalue of a bounded domain \Omega in R^d is bounded
from below
by Vol (\Omega)^{2/d}, for some positive constant C_d
depending on
dimension.
Consider a closed Riemannian manifold of dimension d.
Let u be an
eigenfunction of the LaplaceBeltrami operator with
eigenvalue \lambda.
Every connected component \Omega of $u\neq 0$ is called
a nodal domain
of $u$. It follows from the FaberKrahn inequality that
Vol(\Omega)>= C
\lambda^{d/2}.
A refined question due to Leonid Polterovich is whether
one can inscribe
in \Omega a ball of radius C\lambda^{1/2}.
The answer is positive in dimension two (M., 2006). In
higher dimensions we
show that this is almost true: One can inscribe in
\Omega a ball of radius
C\lambda^{1/2}(\log\lambda)^{(d2)/2}.
I will explain several ideas which go into the proof.
The talk is based on joint work with Philippe Charron.










22.11.2023, 14:10 (Wednesday) 
Vincent Humiliere (Sorbonne University, Paris) 




Title: 
Morse/Floer theory with DGcoefficients and periodic orbits in magnetic
cotangent bundles. 

Location: 
Zoom session 




Abstract: 
In joint work (in progress) with JeanFrançois Barraud, Mihai Damian and
Alexandru Oancea, and building on the work of Barraud and Cornea (2004),
we develop a Morse/Floer theory with coefficients in a DGlocal system.
This allows for instance to recover the homology of a fibration (whose
fiber does not necessarily have finite dimension) from Morse/Floer data
on the base of the fibration. I will present an application to
Hamiltonian dynamics, namely existence results for periodic orbits on
certain energy hypersurfaces in magnetic cotangent bundles. 









29.11.2023, 14:10 (Wednesday) 
Igor Uljarevic (University of Belgrade) 




Title: 
Spectral invariants for a contact Hamiltonian 

Location: 
Zoom session 




Abstract: 
In this talk, I will introduce a persistence
module
associated with a contact Hamiltonian on a fillable
contact manifold
and discuss numerical invariants that can be extracted
from it.
In particular, I will talk about spectral invariants and
their
properties. This talk is based on a joint work with
Danijel Djordjevic
and Jun Zhang. 









06.12.2023, 14:10 (Wednesday) 
Alejandro Vicente (Hebrew University) 




Title: 
Integrable systems, Lagrangian fibrations and
symplectic embedding problems 

Location: 
Zoom session





Abstract: 
Toric domains are a special
class of symplectic manifolds
in C^n, invariant by the standard circle action in each
of the
onedimensional complex planes. This abundance of
symmetries makes
the study of embedding problems into toric domains and
computations of
symplectic capacities of toric domains, often possible.
So when
considering these kinds of problems in general manifolds
(for example:
disk cotangent bundles of surfaces), a strategy could be
to produce
a toric domain out of your given manifold and "reduce"
the original
problem to a similar one in toric domains.
In this talk, I will explain how to carry out this idea
for computing
the biggest ball that can be symplectically embedded
into the disk
cotangent bundle of an ellipsoid of revolution. The idea
to obtain such
a related toric domain comes by studying an integrable
system for the
disk cotangent bundle of an ellipsoid of revolution and
using
Arnol'dLiouville Theorem to obtain actionangle
coordinates. We then
use the obtained toric domain to suggest a candidate to
the best
symplectically embedded ball. Finally, to show that this
is, as a
matter of fact, the best possible ball, we use some
obstructional tools,
more specifically, ECH capacities. This part of the talk
is joint work
with Brayan Ferreira and Vinicius Ramos.
We will also see how to obtain these results from
another point of view,
namely, by using the rotational symmetry to realize
these disk cotangent
bundles as almost toric fibrations. With this last
technique, we will
recover some old results from Vinicius Ramos on the
Lagrangian bidisk
B^2x B^2. Furthermore, we construct some interesting
Lagrangian fibrations
in the Lagragian bidisk B^3x B^3 and the disk cotangent
bundle of S^3.
This is work in progress with Santiago AchigAndrango
and Renato Vianna.










13.12.2023, 17:10 (Wednesday) 
Dylan Cant (University of Montreal)





Title: 
A symplectic cohomology persistence module for
contact isotopies of the ideal boundary of a Liouville
manifold 

Location: 
Zoom session 




Abstract: 
Let W be a Liouville manifold with ideal contact
boundary Y.
It is wellknown that the contact geometry of the Y is
influenced by
the symplectic geometry of W. Notably, every contact
isotopy of Y is
the "ideal restriction" of some Hamiltonian isotopy of
W. The associated
Floer cohomology group depends only on the contact
isotopy. Any contact
isotopy can be "wrapped" by the Reeb flow associated to
a choice of
contact form (the wrapping depends on some parameter),
and the associated
Floer cohomology groups can be organized into a
persistence module.
As one varies the contact isotopy, the resulting barcode
varies
Lipshitzcontinuously with respect to Shelukhin's Hofer
norm (with
Lipshitz constant 1). This structure is used to prove
various
existence results for "translated points," and to
construct
spectral invariants for contactomorphisms. 









20.12.2023, 14:10 (Wednesday) 
Matthias Meiwes
(Tel Aviv University) 




Title: 
Orbit growth in link complements and 3D Reeb flows 

Location: 
Zoom session 




Abstract: 
Recently, Alves and Pirnapasov studied the growth of contact homology in the complement of a link of closed Reeb orbits on contact 3manifolds and discovered orbit forcing phenomena that are special to Reeb flows. Motivated by those findings, they asked a question which can be formulated roughly as follows: Can we, by taking a suitable sequence of links of closed orbits, recover the topological entropy of any 3D Reeb flow by the growth of contact homology in the complement of those links? In this talk, I will explain a result that gives a positive answer to that question for generic Reeb flows. I will also discuss some applications of (variants of) that result. One is in a joint work with M. Alves, L. Dahinden, and A. Pirnapasov where we studied robustness features of the topological entropy of Reeb flows.










27.12.2023, 14:10 (Wednesday) 
Sara Tukachinsky (Tel Aviv University) 




Title: 
Openclosed maps as classifiers in open GromovWitten theory 

Location: 
Zoom session 




Abstract: 
Openclosed maps relate cohomology theories of a symplectic manifold and a Lagrangian submanifold that make use of pseudoholomorphic curves.
Bounding chains are differential forms on a Lagrangian submanifold that solve a particular (MaurerCartan) equation, also involving pseudoholomorphic curves. Such forms are used in defining Lagrangian Floer cohomology and open GromovWitten invariants.
Under nontrivial topological assumptions, a version of the openclosed map turns out to give a full classification of the space of all bounding chains, up to a natural equivalence relation.
Partly based on joint work with Pavel Giterman. 









03.01.2024, 14:10 (Wednesday) 
Iosif Polterovich (University of Montreal) 




Title: 
Stability of isoperimetric eigenvalue inequalities on surfaces 

Location: 
Schreiber 309 and zoom 




Abstract: 
Optimisation of Laplace eigenvalues on Riemannian manifolds is a fascinating topic in spectral geometry.
In the past decade, significant progress has been achieved on maximisation of eigenvalues on surfaces under the area constraint.
I will discuss some recent advances on this subject, with an emphasis on the stability estimates for sharp isoperimetric inequalities.
The talk is based on a joint work with M. Karpukhin, M. Nahon and D. Stern. 









10.01.2024, 14:00 (Wednesday)

Xujia Chen (Harvard University) 




Title: 
Why can Kontsevich's invariants detect exotic phenomena? 

Location: 
Zoom session 




Abstract: 
In topology, the difference between the category of smooth manifolds and the category of topological manifolds has always been a delicate and intriguing problem, called the "exotic phenomena". The recent work of Watanabe (2018) uses the tool "Kontsevich's invariants" to show that the group of diffeomorphisms of the 4dimensional ball, as a topological group, has nontrivial homotopy type. In contrast, the group of homeomorphisms of the 4dimensional ball is contractible. Kontsevich's invariants, defined by Kontsevich in the early 1990s from perturbative ChernSimons theory, are invariants of (certain) 3manifolds / fiber bundles / knots and links (it is the same argument in different settings). Watanabe's work implies that these invariants detect exotic phenomena, and, since then, they have become an important tool in studying the topology of diffeomorphism groups. It is thus natural to ask: how to understand the role smooth structure plays in Kontsevich's invariants? My recent work provides a perspective on this question: the real blowup operations on a smooth manifold depends on the smooth structure in an essential way; thus, the topology of the spaces obtained by doing some blowups on a smooth manifold/fiber bundle X encodes information of the smooth structure on X. 









17.01.2024,
14:00 (Wednesday)

Robert Cardona (University of Barcelona) 




Title: 
Contact topology and timedependent hydrodynamics: nonmixing and spectral invariants 

Location: 
Zoom session 




Abstract: 
The wellknown connection between contact topology and the Euler equations for ideal fluids, introduced in the seminal work of Etnyre and Ghrist, is restricted to the study of stationary solutions, and usually for adapted instead of fixed ambient metrics. In this talk, we broaden the scope of contact hydrodynamics by presenting a new framework that allows assigning contact/symplectic invariants to large sets of timedependent solutions to the Euler equations on any threemanifold with an arbitrary fixed Riemannian metric. Applications include a general nonmixing result for the infinitedimensional dynamical system defined by the equations and the existence of new nontrivial first integrals of the PDE obtained from spectral invariants in embedded contact homology.
This is based on joint work with Francisco Torres de Lizaur. 









24.01.2024, 17:10 (Wednesday) 
Filip Brocic (University of Montreal) 




Title: 
Arnold’s chord conjecture for conormal Legendrian lifts 

Location: 
Zoom session 




Abstract: 
The chord conjecture, due initially to Arnold in the case of the standard contact threesphere, asserts the existence of a Reeb chord with boundary on every closed Legendrian submanifold of a closed contact manifold for every contact form. This conjecture was established in various settings by Cieliebak, Mohnke, Hutchings and Taubes, and others. In this talk, I will sketch a proof of the chord conjecture for conormal bundles of closed submanifolds of any closed manifold seen as Legendrians in the cosphere bundle. This generalizes a result of Grove in Riemannian geometry regarding the existence of geodesics normal to the submanifold. The method of proof involves wrapped Floer cohomology with local coefficients. This talk is based on a joint work with Dylan Cant and Egor Shelukhin.











31.01.2024, 14:10 (Wednesday) 
Sara Tukachinsky (Tel Aviv University) 




Title: 
Relative quantum cohomology of complete intersections 

Location: 
Schreiber 309 and zoom session 




Abstract: 
Quantum cohomology of a symplectic manifold X is the usual cohomology, but with wedge product deformed by adding contributions coming from pseudoholomorphic spheres. Given a Lagrangian submanifold L, there is a relative version of quantum cohomology. It can be thought of as dual to the homology of the complement of L in X. Here, the product is deformed using a combination of pseudoholomorphic spheres and disks.
In this talk, I will recall the above structures, then give explicit computations for the ring structure of relative quantum cohomology of some particularly convenient complete intersections. Joint work with Kai Hugtenburg.










14.02.2024, 14:10 (Wednesday) 
Yoav Zimhony (Tel Aviv University) 




Title: 
Commutative control data for smoothly locally trivial stratified spaces 

Location: 
Schreiber 309 and zoom session 




Abstract: 
For a compact Lie group $G$ and a Hamiltonian $G$space $M$ with momentum map $\mu:M\to \g^*$, we prove that the zero level set $\mu^{1}(0)$ and the critical set $\text{Crit}\norm{\mu}^2$ of the norm squared momentum map are neighbourhood smooth weak deformation retracts.
To this end we show that these subsets, stratified by orbit types, satisfy a condition stronger than Whitney (B) regularity  \textit{smooth local triviality with conical fibers}.
Using this condition we construct control data in the sense of Mather with the additional properties that the fiberwise multiplications by scalars, coming from the tubular neighbourhood structures, preserve strata and commute with each other. We use this control data to obtain the neighbourhood smooth weak deformation retraction.
Finally, such structures for the zero level set $\mu^{1}(0)$ reduce to similar structures for the reduced space $\mu^{1}(0)/G$, yielding a similar result for the reduced space and its stratified subspaces.











27.03.2024, 14:10 (Wednesday) 
Susan Tolman (University of Illinois UrbanaChampaign)





Title: 
NonHamiltonian circle actions with minimal fixed points 

Location: 
Schreiber 309 and zoom session 




Abstract: 
Let the circle act on a closed manifold $M$, preserving a symplectic form $\omega$.
We say that the action is Hamiltonian if there exists a moment map, that is,
a map $\Psi: M \to R$ such that $i_\xi \omega =  d \Psi$, where $\xi$ is
the vector field that generates the action. In this case, a great deal of information about the
manifold is determined by the fixed set. Therefore, it is very important to determine when
symplectic actions are Hamiltonian. There has been a great deal of research on this question. It's easy to see that every
Hamiltonian action has fixed points. McDuff proved that the converse wasn't true by constructing a nonHamiltonian action with fixed tori.
She then raised the following question, usually called the ``McDuff conjecture": Does there exist a nonHamiltonian symplectic circle
action with isolated fixed points on a closed, connected symplectic manifold?
I was able to construct such an example with 32 fixed points, but this raised another question.
What is the minimal number of possible fixed points?
I will discuss my work with D. Jang on reducing the number of fixed points. We have already constructed an example with as
few as 10 fixed points, and are now working on constructing an example with only two fixed points, which is the smallest possible number. 









15.05.2024, 14:10 (Wednesday) 
Victor Ivrii (University of Toronto),
joint session with Analysis seminar 




Title: 
Complete Spectral Asymptotics for Periodic and Almost Periodic Perturbations of Constant Coefficients Operators and BetheSommerfeld Conjecture in Semiclassical Settings 

Location: 
Schreiber 209, no zoom 




Abstract: 
1. Under certain assumption complete semiclassical asymptotic holds for integrated density of states
for periodic and almost periodic perturbations constant coefficient operators.
2. In dimension 2 or higher almost all spectral gaps are missing (in contrast to 1dimension).











22.05.2024, 14:10 (Wednesday) 
Konstantin Khanin (University of Toronto)
Distinguished Lecture in Pure Mathematics 




Title: 
On typical rotation numbers for families of circle maps with singularities 

Location: 
Schreiber 309 and zoom session 




Abstract: 
I shall discuss how one can define in a natural way the notion of
typical rotation numbers for families of circle maps with singularities.
This problem is related to a well known fact that in the case of maps with singularities the set of
parameters, corresponding to irrational rotation numbers, has zero Lebesgue measure.
Our approach is based on the hyperbolicity of renormalizations.
I shall also discuss a natural setting for the Kesten theorem in the case of maps with singularities. 









29.05.2024, 17:10 (Wednesday) 
Andre Neves (University of Chicago)  Blumenthal
Lecture in Geometry 




Title: 
Abundance of minimal hypersurfaces. 

Location: 
Zoom session 




Abstract: 
Minimal surfaces are physical objects which appear naturally in math and applied science. In the 80’s Yau conjectured that any
closed Riemannian manifold should have an infinite number of closed minimal hypersurfaces. For 30 years little progress was made but over the last 10 years a renewed interest on the problem led to its complete solution.
I will survey the results, the new ingredients, and the current state of the art.










05.06.2024, 14:10 (Wednesday) 
Jean Gutt (University of Toulouse and INU Champollion) 




Title: 
Coarse distance from dynamically convex to convex 

Location: 
Zoom session 




Abstract: 
Chaidez and Edtmair have recently found the first examples of dynamically
convex domains in R^4 that are not symplectomorphic to convex domains
(called symplectically convex domains), answering a longstanding open
question. In this talk we shall present new examples of such domains
without referring to ChaidezEdtmair’s criterion. We shall show that
these domains are arbitrarily far from the set of symplectically convex
domains in R^4 with respect to the coarse symplectic BanachMazur distance
by using an explicit numerical criterion for symplectic nonconvexity.
This is joint work with J.Dardennes, V.Ramos and J.Zhang. 












19.06.2024, 14:10 (Wednesday) 
Baptiste Serraille (Orsay) 




Title: 
The sharp C^0fragmentation property for Hamiltonian
diffeomorphisms and homeomorphisms on surfaces


Location: 
Room 309 and zoom session





Abstract: 
Fragmentation properties have been used by Banyaga, Fathi
and
Thurston in order to study the algebraic structure of groups of
diffeomorphisms, volume preserving diffeomorphisms/homeomorphisms and
Hamiltonian diffeomorphisms. This property has been improved on
surfaces
by Entov, Polterovich and Py and later by Seyfaddini in order to give
better control on the "fragments". Still on surfaces, I will present a
sharper version of those results.










26.06.2024, 14:10 (Wednesday) 
Lenya Ryzhik (Stanford)  MINT Distinguished Lecture 




Title: 
Diffusion of knowledge and the state lottery society


Location: 
Room 309 and zoom session





Abstract: 
Diffusion of knowledge models in macroeconomics describe the evolution of an interacting system
of agents who perform individual Brownian motions (this is internal innovation) but also can jump on top
of each other (this is an agent or a company acquiring knowledge from another agent or company). The learning
strategy of the individual agents (jump probabilities) are obtained from an additional optimization problem that involves
the current configuration of particles and is a solution to a forwardbackwards in time meanfield game. We will discuss
some preliminary results on the basic properties of this system.










26.06.2024, 17:10 (Wednesday) 
Egor Shelukhin (Universite de Montreal) 




Title: 
A symplectic HilbertSmith conjecture


Location: 
Zoom session





Abstract: 
I will discuss a
recent
proof of new cases of the HilbertSmith conjecture for actions by homeomorphisms of symplectic nature.
It rules out faithful actions of the additive padic group and provides further obstructions to group actions
in symplectic topology. The proof relies on a new approach to this circle of questions
combined with power operations in Floer cohomology and quantitative symplectic topology.










2.07.2024, 14:10 (Tuesday) 
Lenya Ryzhik (Stanford)  MINT Distinguished Lecture, joint with Analysis seminar 




Title: 
Shape defect function and convergence to traveling waves


Location: 
Room 209





Abstract: 
It is well known that solutions to many semilinear parabolic equations
can be interpreted in terms of various functionals of branching Brownian
motion, most famously so for the FisherKPP equation. The shape defect
function is a recently reinvented convenient PDE tool that allows to analyze the convergence
of the solutions to traveling waves in a very straightforward fashion. Surprisingly,
its behavior looks anomalous in the BBM context.










3.07.2024, 14:10 (Wednesday) 
Lev Buhovsky (TAU) 




Title: 
Asymptotic Hofer geometry on surfaces


Location: 
Room 309 and zoom session





Abstract: 
The growth of the Hofer norm of iterations of a Hamiltonian diffeomorphism is still not
well understood in general. In all known examples where the growth is not asymptotically linear,
it appears to be bounded. This dichotomy phenomenon was previously demonstrated by Polterovich and Siburg
for autonomous diffeomorphisms on (open) connected surfaces of infinite area.
In my talk, I will discuss a new approach that extends this result to the 2sphere and potentially to other closed surfaces.
Based on a joint work in progress with Ben Feuerstein, Leonid Polterovich and Egor Shelukhin.










10.07.2024, 14:10 (Wednesday) 
Marco Mazzucchelli (ENS Lyon) 




Title: 
Locally maximal closed orbits of Reeb flows


Location: 
Zoom session





Abstract: 
A compact invariant set of a flow is called locally maximal when it is the largest invariant set in some neighborhood. In this talk, based on joint work with Erman Cineli, Viktor Ginzburg, and Basak Gurel, I will present a "forced existence" result for the closed orbits of certain Reeb flows on spheres of arbitrary odd dimension:
 If the contact form is nondegenerate and dynamically convex, the presence of a locally maximal closed orbit implies the existence of infinitely many closed orbits.
 If the locally maximal closed orbit is hyperbolic, the assertion of the previous point also holds without the nondegeneracy and with a milder dynamically convexity assumption.
These statements extend to the Reeb setting earlier results of Le CalvezYoccoz for surface diffeomorphisms, and of GinzburgGurel for Hamiltonian diffeomorphisms of certain closed symplectic manifolds.










24.07.2024, 14:10 (Wednesday) 
Pazit HaimKislev (TAU) 




Title: 
TBA


Location: 
Room 309 and zoom session





Abstract: 
TBA










31.07.2024, 14:1015:00 (Wednesday) 
Adi Dickstein (TAU) 




Title: 
TBA


Location: 
Room 309 and zoom session





Abstract: 
TBA










31.07.2024, 15:1016:00 (Wednesday) 
Oleg Sheinman (Steklov Mathematical Institute, Moscow) 




Title: 
On reversion of the AbelPrym map and its applications to integrable
systems


Location: 
Room 309 and zoom session





Abstract: 
Abel map transfoms a certain symmetric power of a Riemann surface to an
Abelian variety called Jacobian of the Riemann surface. In the theory of
integrable systems Abel map appeared as early as in Jacobi's "Lectures
on dynamics". In frame of the method of Separation of Variables, the
phase space of the system exfoliates into symmetric products of curves.
We will consider the case when those curves are algebraic. Then the Abel
map transforms that foliation into the Lagrangian foliation of the
system. It is wellknown that the trajectories of integrable systems are
straight line windings of the Lagrangian tori (the fibers of the last
foliation). To get trajectories explicitly, in the original separation
coordinates, we need to reverse the Abel map. This problem is known as
Jacobi inversion problem. Its solution is classical for Jacobians.
However, for majority of classical and new integrable systems Lagrangian
tori are not Jacobians but different Abelian varieties called Prym
varieties, or Prymians. In general, no analog of Jacobi inversion can be
formulated for Prymians. We hilight the case when the last nevertheless
is possible. As application, we represent the corresponding Prymians as
symmetric powers of certain curves, and resolve some Hitchin systems in
theta functions. All algebraic geometry preliminaries will be explained.










7.08.2024, 14:10 (Wednesday) 
Matthias Meiwes (TAU) 




Title: 
TBA


Location: 
Room 309 and zoom session





Abstract: 
TBA






