Geometry & Dynamics Seminar 2017-18


The seminar will take place in Schreiber Building room 309, on Wednesdays at 14:10.

Please check each announcement since this is sometimes changed.

 

Upcoming Talks        Previous Talks        Previous Years











25.10.2017, 14:10 (Wednesday) Orientation meeting for students




Location: Schreiber bldg., room 309, Tel-Aviv University




31.10.2017,12:10 (Tuesday)

SPECIAL LECTURE - PLEASE NOTE THE DATE,  PLACE & TIME

Jean-Michel Bismut, Université Paris-Sud (Orsay)




Title:
Hypoelliptic Laplacian, index theory and the trace formula
Location: Schreiber bldg., room 209, Tel-Aviv University



Abstract: The hypoelliptic Laplacian is a family of operators, indexed by $b\in
\mathbf{R}_{+}^{*}$, acting on the
total space of the tangent  bundle of a Riemannian manifold, that
interpolates between the ordinary Laplacian as $b\to 0$ and the
generator of the geodesic flow as $b\to + \infty $.  These operators
are not elliptic, they are not self-adjoint, they are hypoelliptic.

The hypoelliptic deformation preserves subtle invariants of the
Laplacian. In the case of locally symmetric spaces, the deformation
is essentially isospectral.

In a first part of the talk, I will describe the geometric
construction of the hypoelliptic Laplacian in the context of de Rham
theory. In a second part, I will explain applications to the trace
formula.









01.11.2017, 14:10 (Wednesday) Daniel Rosen (TAU) 



Title: Duality of Caustics in Minkowski Billiards
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: Mathematical billiards are a classical and well-studied class of dynamical systems,
"a mathematician’s playground". Convex caustics, which are curves to which billiard
trajectories remain forever tangent, play an important role in the study of billiards.
In this talk we will discuss convex caustic in Minkowski billiards, which is the
generalization of classical billiards no non-Euclidean normed planes. In this case a
natural duality arises from, roughly speaking,  interchanging the roles of the billiard
table and the unit ball of the (dual) norm. This leads to duality of caustics in Minkowski
billiards. Such a pair of caustics is dual in a strong sense, and in particular they have
equal perimeters and other classical parameters. We will show that, when the norm is
Euclidean, every caustic possesses a dual caustic, but in general this phenomenon fails.
Based on joint work with S. Artstein-Avidan, D. Florentin, and Y. Ostrover .








08.11.2017, 14:10 (Wednesday)
Mads Bisgaard (ETH)




Title: Topology of small Lagrangian cobordisms
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: I will discuss how one can study Lagrangian cobordisms from the point
of view of quantitative symplectic topology: It turns out that if a Lagrangian
cobordism is sufficiently small (in a sense which can be made precise), then
its topology is to a large extend determined by its boundary. I will show how
this principle allows one to derive several homological uniqueness results for
small Lagrangian cobordisms. In particular (under the smallness assumption)
I will prove homological uniqueness of the class of Lagrangian cobordisms which,
by Biran-Cornea’s Lagrangian cobordism theory, induces operations on a version
of the derived Fukaya category. If time permits it, I will indicate a link from these
ideas to Vassilyev’s theory of Lagrange characteristic classes and the classification
of caustics.








15.11.2017, 14:10 (Wednesday) Dmitry Novikov (Weizmann Institute)



Title: Complex cellular parameterization
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: We introduce the notion of a complex cell, a complex analog
of the cell decompositions used in real algebraic and analytic
geometry. Complex cells defined using holomorphic data admit a
natural notion of analytic continuation called $\delta$-extension,
which gives rise to a rich hyperbolic geometric structure absent in
the real case. We use this structure to prove that complex cellular
decompositions share some interesting features with the classical
constructions in the theory of resolution of singularities. Restriction
of a complex cellular decomposition to the reals recovers the preparation
theorem for subanalytic functions, and can be viewed as an analytic
continuation thereof.

A key difference in comparison to the classical resolution of
singularities is that the cellular decompositions are intrinsically
uniform over (sub)analytic families. We deduce a subanalytic version
of the Yomdin-Gromov theorem where $C^k$-smooth
maps are replaced by mild maps.

(joint work with Gal Binyamini)








22.11.2017, 14:10 (Wednesday) Boris Kruglikov (University of Tromsø)




Title: Integrability in Grassmann geometry and twistor theory
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: This reviews a series of works joint with E.Ferapontov, D.Calderbank,
B.Doubrov and V.Novikov. It will be explained that for several important
classes of PDEs the integrability by the method of hydrodynamic reductions
is equivalent to a Lax representation. This includes equations of Hirota type
and also PDE systems encoded by submanifolds in Grassmannians. For the
latter the integrability can be interpreted geometrically. In 3D and 4D the
integrability is also shown to be equivalent to Einstein-Weyl and, respectively,
self-dual geometry on solutions. This relates dispersionless integrability to the
twistor theory.
Ref: J.Diff.Geom.97 (2014), arXiv:1503.02274, arXiv:1612.02753, arXiv:1705.06999.








29.11.2017, 14:10 (Wednesday) Igor Uljarevic




Title: Floer homology and contact Hamiltonians
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: In the setting of symplectic manifolds which are convex at infinity,
we use a version of the Aleksandrov maximum principle to extend the class of
Hamiltonians that one can use in the direct limit when constructing symplectic
homology. As an application, we detect elements of infinite order in the symplectic
mapping class group of a Liouville domain and prove existence results for
translated points.
The talk is based on joint work with W. Merry.








06.12.2017, 14:10 (Wednesday) Dmitry Faifman (University of Toronto)



Title: Contact curvatures and integral geometry of the contact sphere
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: Valuations are finitely additive measures on nice subsets, for example
the Euler characteristic, volume and surface area are valuations. During
the 20th century, valuations have been studied predominantly on convex
bodies and polytopes, in linear spaces and lattices. Valuations on manifolds
were introduced about 15 years ago by S. Alesker, with contributions by
A. Bernig, J. Fu and others, and immediately brought under one umbrella a
range of classical results in Riemannian geometry, notably Weyl's tube
formula and the Chern-Gauss-Bonnet theorem. These results circle around
the real orthogonal group. In the talk, the real symplectic group will be the
central player. Drawing inspiration from the Lipschitz-Killing curvatures in
the Riemannian setting, we will construct some natural valuations on contact
and almost contact manifolds, which generalized the Gaussian curvature.
We will also construct symplectic-invariant distributions on the grassmannian,
leading to Crofton-type formulas on the contact sphere and symplectic space.








13.12.2017, 14:10 (Wednesday) Sergey Fomin (University of Michigan) - MINT distinguished lecture




Title: Morsifications and mutations
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: I will discuss a surprising connection between singularity theory and cluster algebras, more specifically
between (1) the topology of isolated singularities of plane curves and (2) the mutation equivalence of the
quivers associated with their morsifications. Joint work with Pavlo Pylyavskyy and Eugenii Shustin.








20.12.2017, 14:10 (Wednesday) NO SEMINAR THIS WEEK










27.12.2017, 14:10 - 15:00 (Wednesday) Kei Irie (Kyoto University and Simons Center for Geometry and Physics)




Title: Denseness of minimal hypersurfaces for generic metrics
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: We prove that, on a smooth closed manifold of dimension $3 \le d \le 7$
with a $C^\infty$-generic Riemannian metric, the union of closed embedded
minimal hypersurfaces is dense. This is joint work with F.Marques and A.Neves.

The proof is based on min-max theory for the volume functional on the space of
codimension 1 (flat) cycles,  which was originally developed by Almgren and Pitts.
The key ingredient of the proof is the ``Weyl law''(proved by Liokumovich, Marques and Neves),
which says that the asymptotic of min-max values in this theory recovers the volume of a
Riemannian manifold.







27.12.2017, 15:10 - 16:00 (Wednesday) Iosif Polterovich (Université de Montréal) 



Title: Isoperimetric inequalities for Laplace eigenvalues on surfaces: some recent developments
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: Isoperimetric inequalities for Laplace eigenvalues have a long history,
going back to the celebrated Rayleigh-Faber-Krahn inequality for the fundamental tone.
Still, many basic questions remain unanswered, particularly, for higher eigenvalues.
In the talk I will give an overview of some recent developments in the study of
isoperimetric inequalities for eigenvalues on compact surfaces with a Riemannian metric.
In particular, I will discuss a solution of a conjecture posed by N. Nadirashvili in 2002
regarding the maximization of higher Laplace-Beltrami eigenvalues on the sphere
(joint with M. Karpukhin, N. Nadirashvili and A. Penskoi).








03.01.2018, 14:10 (Wednesday) Julian Chaidez (University of California, Berkeley) 



Title: The Conley-Zehnder Index In Singular Contact Geometry
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: The Conley-Zehnder (CZ) index is an important invariant of closed orbits of smooth
Hamiltonian flows and Reeb flows. In this talk, I will discuss a version of the CZ index
for various "singular" contact geometry problems, such as Reeb dynamics on polytopes
and dynamical billiards. We will show how this CZ index can be applied to convert some
results in smooth contact geometry into results about singular contact geometry using a
limiting argument.








10.01.2018, 14:00 (Wednesday)
Pazit Haim-Kislev (TAU)



Title: The EHZ capacity of convex polytopes
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: The EHZ capacity is a well-studied symplectic invariant that measures the "symplectic size"
of convex sets, by taking the minimal action of a closed characteristic on the boundary.
We introduce a simplification to the problem of finding a closed characteristic with minimal
action for the case of convex polytopes. We use this to give a combinatorial formula for the
EHZ capacity of convex polytopes, and to prove a certain subadditivity property of the capacity
of a general convex body.








17.01.2018, 14:10 (Wednesday) Daniel Alvarez-Gavela (Stanford University)




Title: Singularities of fronts and their simplification
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: We will present a full h-principle for the simplification of
singularities of Lagrangian and Legendrian fronts. We give several
applications to symplectic and contact topology, including relations to
pseudo-isotopy theory and to Nadler's program for the arborealization of
Lagrangian skeleta.








07.03.2018, 14:10 (Wednesday) TBA



Title: TBA
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: TBA







14.03.2018, 14:10 (Wednesday) TBA



Title: TBA
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: TBA







21.03.2018, 14:10 (Wednesday) RESERVED




Title: TBA
Location: Schreiber bldg., room 309, Tel-Aviv University 



Abstract: TBA







28.03.2018, 14:10 (Wednesday) TBA



Title: TBA
Location: Schreiber bldg., room 309, Tel-Aviv University




Abstract: TBA







11.04.2018, 14:10 (Wednesday) Jarek Kedra (University of Aberdeen)




Title: TBA
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: TBA







25.04.2018, 14:10 (Wednesday) TBA



Title: TBA
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: TBA







Workshop: Topological data analysis meets symplectic topology

NO SEMINAR THIS WEEK!










09.05.2018, 14:10 (Wednesday) TBA



Title: TBA
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: TBA







16.05.2018, 14:10 (Wednesday) TBA



Title: TBA
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: TBA







23.05.2018, 14:10 (Wednesday) TBA



Title: TBA
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: TBA







30.05.2018, 14:10 (Wednesday)
TBA



Title: TBA
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: TBA







06.06.2018, 14:10 (Wednesday) TBA



Title: TBA
Location: Schreiber bldg., room 309, Tel-Aviv University




Abstract: TBA










13.06.2018, 14:10 (Wednesday) TBA



Title: TBA


Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: TBA















Organized by Misha Bialy, Lev Buhovsky, Yaron Ostrover, and Leonid Polterovich