Geometry & Dynamics Seminar 2018-19


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











17.10.2018, 14:10 (Wednesday) Orientation meeting for students




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







24.10.2018, 14:10 (Wednesday)
Chandrika Sadanand (Technion)




Title:
You can hear the shape of a polygonal billiard table
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: Consider a polygon-shaped billiard table on which a ball can roll
along straight lines and reflect off of edges infinitely. In work joint with
Moon Duchin, Viveka Erlandsson and Chris Leininger, we have characterized the
relationship between the shape of a polygonal billiard table and the set of
possible infinite edge itineraries of balls travelling on it. In this talk, we will
explore this relationship and the tools used in our characterization (notably a new
rigidity result for flat cone metrics).









31.10.2018, 14:10 (Wednesday) Louis Ioos (Tel Aviv University)



Title: Geometric Quantization of Hamiltonian flows
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: Quantum mechanics is a physical theory that describes nature at the scale
of atoms, and one of its fundamental aspects is its relation with classical mechanics,
which describes nature at human scales. In particular, there are general axioms
that a quantum theory must satisfy coming from its classical counterpart. The
Geometric Quantization program is an attempt to implement these
axioms in the general framework of symplectic geometry. In this talk, I will present
how one constructs the quantum evolution operator associated to a given
Hamiltonian flow in this context, and I will give estimates on its behavior at the limit
of large scales.









07.11.2018, 14:10 (Wednesday)
Michael Khanevsky (Technion)




Title: Surface quasimorphisms and the Hofer norm
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: We consider several constructions of quasimorphisms on the Hamiltonian group of
surfaces that were proposed by Gambaudo-Ghys, Polterovich and Py. These
constructions are based on topological invariants either of individual orbits or of
orbits of finite configurations of points and a quasimorphism computes the average
value of such invariant in the surface. We show that many quasimorphisms that arise
this way are not Hofer continuous.








14.11.2018, 14:10 (Wednesday) Bo'az Klartag (Weizmann Institute of Science)



Title: Convex geometry and waist inequalities
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: We will discuss connections between Gromov's work on isoperimetry of waists
and Milman's work on the M-ellipsoid of a convex body.
It is proven that any convex body K in an n-dimensional Euclidean space has a
linear image K_1 of volume one satisfying the following
waist inequality: Any continuous map f from K_1 to R^d has a fiber f^{-1}(t)
whose (n-d)-dimensional volume is at least c^{n-d}, where c > 0
is a universal constant. Already in the case where f is linear, this constitutes a
slight improvement over known results.
In the specific case where K = [0,1]^n, one may take K_1=K and c=1, confirming
a conjecture by Guth. We furthermore exhibit relations
between waist inequalities and various geometric characteristics of the convex body K.









21.11.2018, 14:10 (Wednesday) Nicolina Istrati (Tel Aviv University)



Title: Toric locally conformally Kahler manifolds
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: A basic problem in geometry is the search of good metrics. On complex manifolds,
a most satisfactory class is given by the Kahler metrics, because of the interplay they
encode between complex, symplectic and Riemannian geometry. However, there are
well-known obstructions to their existence; we are then led to consider new classes
which would imitate their good behavior. One way to do this is to consider their
conformal analogue, the locally conformally Kahler (LCK) metrics. A Hermitian metric
g on a complex manifold is LCK if around every point there exists a local Kahler metric
which is conformal to g. The symplectic counterpart of these structures is given by the
locally conformally symplectic (LCS) forms.

In the first part of this talk, I will give an introduction to this class of manifolds and
present some of their main features. Then I will focus on toric LCS manifolds, which
can be defined in analogy with toric symplectic geometry. I will present a classification
result in terms of moment polytopes for the toric LCS manifolds which admit
compatible complex structures.








28.11.2018, 14:10 (Wednesday) Yaniv Ganor (Tel Aviv University)




Title: Tropical Approach to Enumerative Algebraic Geometry
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: Enumerative algebraic geometry is a branch of algebraic geometry that studies
problems of counting the number of geometric objects in come class subject to
geometric constraints. For example,  we all know that the number of lines in
the plane, passing through a pair of distinct points is one.

Tropical geometry studies a certain degeneration of complex algebraic
geometry, where the complex objects degenerate into some polyhedral complexes.
It can be seen as an analogue of algebraic geometry over the tropical semiring,
roughly amounting to replacing addition with maximum and multiplication
with addition.

The tropical approach to enumerative geometry, pioneered by Mikhalkin, is to
degenerate complex objects into tropical objects, count the tropical
counterparts, which is generally easier, due to their piecewise linear
nature, and then lift them back to complex algebraic objects.

In this talk we will survey tropical geometry of curves in the plane
and its applications to the count of complex curves on complex surfaces,
via an algebraic approach due to Shustin. Then we will present some results
in the count of singular complex curves, a joint work with Eugenii Shustin.

We will assume no previous knowledge of tropical geometry nor of algebraic geometry.








05.12.2018, 14:10 (Wednesday) Ram Band (Technion)




Title: Neumann domains on manifolds and graphs
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: The nodal set of a Laplacian eigenfunction forms a partition of the
underlying manifold or graph. Another natural partition is based on
the gradient vector field of the eigenfunction (on a manifold) or on
the extremal points of the eigenfunction (on a graph).The submanifolds
(or subgraphs) of this partition are called Neumann domains. We present
some interesting results concerning Neumann domains on manifolds and on
graphs. We compare manifolds to graphs in this sense and also relate
the Neumann domain results to the nodal domain study.

The talk is based on joint works with Lior Alon, Michael Bersudsky,
Sebastian Egger, David Fajman and Alexander Taylor.








12.12.2018, 14:10 (Wednesday) Misha Verbitsky (IMPA)




Title: Multiplicity of singularities is not a bi-Lipschitz invariant
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: Zariski has conjectured that multiplicity of a singularity
of a hypersurface is a homeomorphism invariant. This conjecture
is still unknown. However, a bi-Lipschitz version of Zariski
conjecture is true: multiplicity of bi-Lipschitz hypersurface
singularities is equal (Comte). The same is also true for
surface singuarities (Newmann-Pichon). It was conjectured that
the multiplicity is a bi-Lipschitz invariant for singularity
of any codimension. Using classification of 5-manifolds, I
would explain how to construct bi-Lipschitz equivalent
singularities of any multiplicity, disproving this conjecture.
This is a joint work with Lev Birbrair, Alexandre Fernandes
and J. Edson Sampaio.








19.12.2018, 14:10 (Wednesday) Oleg Ivrii (Caltech)




Title: Complex dynamics, dimensions of quasicircles and the Weil-Petersson metric
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: I will begin this talk by recalling the classical Weil-Petersson 
metric on Teichmüller space. McMullen showed that the Weil-Petersson
metric is related to the second derivative of the Hausdorff dimensions 
of certain quasicircles arising from simultaneous uniformization.
A similar construction can be carried out for matings of Blaschke 
products, which allows one to define a Weil-Petersson metric on
the main cardioid of the Mandelbrot set.

In my PhD thesis, I studied the Weil-Petersson metric in degree 2 and 
showed that the metric is incomplete and made some progress towards
understanding its metric completion (which is an analogue of the
Deligne-Mumford compactification). Together with K. Astala,
A. Perälä and I. Prause, we used fractal approximation techniques to 
understand dimensions of general quasicircles, that is, we used
dynamical methods to study extremal problems in conformal mapping.
I hope to give a brief overview of these developments.

Here are some pictures related to the talk.








26.12.2018, 14:10 (Wednesday) Albert Fathi (Georgia Tech)



Title: Singularities of solutions of the Hamilton-Jacobi equation.
A toy model: distance to a closed subset.

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



Abstract: ABSTRACT







02.01.2019, 14:10-15:00 (Wednesday)
Egor Shelukhin (University of Montreal)



Title: Upper bounds on the Lagrangian spectral norm
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: We discuss recent developments in establishing uniform bounds
on the spectral norm and related invariants of Lagrangian
submanifolds of open and closed symplectic manifolds.
Furthermore, we outline a few applications. This talk is
partially based on joint work with Asaf Kislev.







02.01.2019, 15:10-16:00 (Wednesday) Alexander Bobenko (Technical University of Berlin)




Title: On a discretization of confocal quadrics:
Geometric parametrizations, integrable systems and incircular nets

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



Abstract: We propose a discretization of classical confocal coordinates. It is
based on a novel characterization thereof as factorizable orthogonal
coordinate systems. Our geometric discretization leads to factorizable
discrete nets with a novel discrete analog of the orthogonality
property. A discrete confocal coordinate system may be constructed
geometrically via polarity with respect to a sequence of classical
confocal quadrics. The coordinate functions of discrete confocal
quadrics are computed explicitly. The theory is illustrated with a
variety of examples in two and three dimensions. These include confocal
coordinate systems parametrized in terms of Jacobi elliptic functions.
Connections with incircular nets and elliptic billiards are established.









09.01.2019, 14:10 (Wednesday)
Daniel Tsodikovich (Tel Aviv University)



Title: Hamiltonian Dynamics on Simplexes
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: In this talk I will discuss the Hamiltonian dynamics on the
four-dimensional standard simplex, in particular the classical
dynamical properties, such as transitivity, integrability,
existence of periodic points, and entropy (some of the
results are generalized to weighted standard simplexes in
any dimension). I will explain how to find the periodic
points and the integrals of motion, and will prove that
the entropy is zero. The talk will show that the standard
simplex exhibits a mixture of chaotic and non-chaotic
properties.








27.02.2019, 14:10 (Wednesday) TBA



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



Abstract: TBA







06.03.2019, 14:10 (Wednesday) TBA



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



Abstract: TBA







13.03.2019, 14:10 (Wednesday) Marcelo Alves (ULB Brussels)



Title: TBA
Location: Schreiber bldg., room309, Tel-Aviv University



Abstract: TBA







20.03.2019, 14:10 (Wednesday) TBA




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



Abstract: TBA







27.03.2019, 14:10 (Wednesday) TBA



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




Abstract: TBA







03.04.2019, 14:10 (Wednesday) TBA



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



Abstract: TBA







10.04.2019, 14:10 (Wednesday) TBA



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



Abstract: TBA







17.04.2019, 14:10 (Wednesday) TBA



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



Abstract: TBA







01.05.2019, 14:10 (Wednesday) TBA



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



Abstract: TBA







Conference: C^0 aspects of symplectic geometry and Hamiltonian dynamics, May 12-16.

NO SEMINAR THIS WEEK!








22.05.2019, 14:10 (Wednesday) David Fisher (Indiana University, Bloomington, USA) - TIDY Distinguished Lecture



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



Abstract: TBA







29.05.2019, 14:10 (Wednesday) Gang Tian  (Peking University, Princeton University) - Blumenthal Lecture in Geometry



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



Abstract: TBA







05.06.2019, 14:10 (Wednesday) Gerhard Knieper (Ruhr-Universitat Bochum) - TIDY Distinguished Lecture



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




Abstract: TBA










12.06.2019, 14:10 (Wednesday) Henri Berestycki (EHESS, Paris)



Title: TBA

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



Abstract: TBA
















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