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) Vukasin Stojisavljevic (Tel Aviv University)




Title: Symplectic Banach-Mazur distance and persistence modules
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: We will define a distance, called symplectic Banach-Mazur distance,
on the space 𝒞M of all "nice" star-shaped domains inside the
cotangent bundle of a smooth manifold M. Our main goal
is to study large-scale geometry of the space 𝒞M equiped with
this distance when M is a closed surface of positive
genus. The key technical ingredient which we use is stability of
persistence modules coming from filtered symplectic homology with
respect to this distance. We will also show certain results related
to the study of closed geodesics. The talk is based on a joint work
with Jun Zhang.









06.03.2019, 14:10 (Wednesday) Louis Ioos (Tel Aviv University)



Title: Canonical Kähler metrics and quantization
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: The search for canonical Kähler metrics on projective manifolds
is one of the fundamental problems in algebraic geometry. In the
beginning of the century, Donaldson discovered a link between this
problem and a geometric point of view on quantum mechanics proposed
by Berezin in the seventies. In this talk, I will explain this link
via the point of view of Positive Operator Valued Measures, and show
how these can be applied to Donaldson's program. This talk is based
on a joint work with Victoria Kaminker, Leonid Polterovich
and Dor Shmoish.








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



Title: Periodic motions and forcing of positive entropy for Reeb flows
Location: Schreiber bldg., room309, Tel-Aviv University



Abstract: A celebrated theorem of Li-Yorke states that a continuous map
of the interval possessing a period three periodic point admits a subset
where the dynamics is chaotic. I will present a related result for Reeb
flows on contact 3-manifolds: the existence of certain periodic orbits
implies positivity of topological entropy. This generalizes a beautiful
result of Denvir and Mackay which asserts that a geodesic flow on the
2-torus with a simple contractible closed geodesic has positive topological
entropy, and is a joint work with Pedro Salomão and Umberto Hryniewicz.
I will also explain some ongoing work with Abror Pirnapasov aimed at
finding infinitely many distinct links in the three torus which force
positive topological entropy.
If time allows I will discuss some (to the best of my knowledge) open
problems on the forcing of slow entropy of Reeb flows and symplectomorphisms,
which are motivated by works of Polterovich and Frauenfelder-Schlenk, and
explain an approach to investigate them based on work of Matthias Meiwes.








20.03.2019, 14:10 (Wednesday) Jordan Payette (University of Montreal)




Title: The representation problem of symplectic submersions
Location: Schreiber bldg., room 309, Tel-Aviv University 



Abstract: Symplectic submersions are functions between symplectic
manifolds which generalize symplectomorphisms. One motivation for their
study resides in the fact that Gromov's non-squeezing theorem for
symplectic embeddings of balls in R^{2n} admits a simple and somewhat
more intrinsic formulation in terms of such functions. From this
perspective, it seems natural to ask which symplectic submersions are
subject to a non-squeezing phenomenon. A starting point is to
characterize those symplectic submersions which appear in Gromov's
theorem; this is what we call the "representation problem". The main
goals of this talk is to introduce the notion of symplectic submersions
and to provide partial solutions to the representation problem; for
instance, the symplectic submersions appearing in Gromov's theorem are
in a sense the simplest ones.








27.03.2019, 14:10 (Wednesday) Michael Brandenbursky (Ben-Gurion University)




Title: Fragmentation norm and relative quasimorphisms
Location: Schreiber bldg., room 309, Tel-Aviv University




Abstract: We prove that manifolds with complicated enough fundamental group
admit measure-preserving homeomorphisms which have positive stable
fragmentation norm with respect to balls of bounded measure.
This is a joint work with Jarek Kedra.








03.04.2019, 14:10 (Wednesday) Misha Bialy (Tel Aviv University)




Title: Geometry of Gutkin billiard tables
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: Eugene Gutkin invented a class of planar Birkhoff billiards with
remarkable invariant curves. It is natural question to ask if there
exist Gutkin billiard tables in higher dimensions. It turns out that
the only higher-dimensional convex billiards with Gutkin property
are round spheres. In the first part of the talk I am going to explain
this result. In the second part (joint with Andrey Mironov and Lior
Shalom), I will discuss the so called Outer billiards and will show
an example of outer billiard with Gutkin property. The dynamics of
this example seems to be very interesting.








10.04.2019, 14:10-15:00 (Wednesday) Amit Wolecki (Tel Aviv University)




Title: Illumination and blocking in rational billiards
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: Does a light source in a polygonal mirror room illuminate the whole
region? Are there pairs of points in a mirror room that do not
illuminate each other?
Examples for a polygonal room that affirms the latter question were
found by Tokarsky in 1995 and raised the question of possible
cardinality of pairs of points that do not illuminate each other.
Breakthrough results by Eskin, Mirzakhani and Mohammadi paved the
way for solving classical illumination problems within the general
framework of flat surfaces and dynamics on the their moduli spaces.
We shall see some of the general results that stems from Eskin
Mirzakhani and Mokhammadi's works and applied for solving problems
in illumination, including a recent result about the cardinality
of non-illuminating pairs or points.







10.04.2019, 15:10-16:00 (Wednesday) Jarek Kedra (University of Aberdeen)




Title: The geometry of the fundamental group
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: It is a classical observation due to John Milnor and Albert Schwarz
that the word metric on the fundamental group of a closed manifold
carries an information about the Riemannian metric of the universal
cover (the metrics are quasi-isometric).  In the above approach the
word metric on the fundamental group is associated with a finite
generating set.

In the talk I will explore the word metrics on the fundamental group
associated with geometrically meaningful generating sets. Specifically,
I will focus on the elements of the fundamental group represented by
closed geodesics and on examples of Riemannian manifolds where such
elements generate the fundamental group. I will then ask the most
basic question whether the diameter of such a word metric is finite
or infinite. The first answer is interpreted as abundance of closed
geodesics while the second as their scarcity.  I will then present
examples for both cases (they are locally symmetric spaces).

This is a join work with Bastien Karlhofer, Michał Marcinkowski and
Alexander Trost.








17.04.2019, 14:10-15:00 (Wednesday) Brian Tervil (University of Haifa)



Title: Translated points for prequantization spaces over monotone toric manifolds
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: I will present a version of Sandon's conjecture on the number of
translated points of contactomorphisms in the context of
prequantization bundles over monotone toric manifolds.
I will outline the construction of a natural prequantization space
for which the conjecture holds, as well as of a cohomology group
which is the main character in the proof of the theorem. The
cohomological construction is based on the theory of generating
functions and equivariant cohomology as developed by Givental
for toric manifolds.







17.04.2019, 15:10-16:00 (Wednesday) Yohann Le Floch (University of Strasbourg)



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



Abstract: Semitoric systems form a class of integrable systems generalizing
toric systems in dimension four, for which one of the integrals
generates acircle action. Their classification was obtained by
Pelayo and Vu Ngoc (2009-2011) in terms of five symplectic
invariants. However, some problems remain: firstly, the construction
of a semitoric system with prescribed invariants is quite involved,
and secondly, few explicit examples of such systems are known.

In the first part of the talk, I will review toric and semitoric
integrable systems. In the second part, I will discuss some
progress towards the explicit construction of a semitoric system
given part of its symplectic invariants, and describe some new
explicit examples. This is based on joint work with Joseph Palmer (Rutgers).








01.05.2019, 14:10 (Wednesday) Weiwei Wu (University of Georgia)




Title: Semi-toric spherical systems and symplectomorphism groups
Location: Schreiber bldg., room 309, Tel-Aviv University



Abstract: We will explain a generalization of semi-toric systems. In dimension
four, such systems can be easily obtained by generalizing the notion of
"toric blow-up". As it turns out, this construction gains new understandings
of the symplectic mapping class groups.  We will explain its relation to a
long-standing question between Lagrangian Dehn twists and symplectic mapping class groups of rational manifolds, and potential construction of exotic finite group actions. This is a combination of several on-going joint works with Liat Kessler, Jun Li and Tian-Jun Li.








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

NO SEMINAR THIS WEEK!








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



Title: Zimmer's conjecture: subexponential growth, measure rigidity and strong
property (T)

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



Abstract: This talk is a sequel to the colloquium of Monday.  I will
try to make it logically independent and self-contained, but most
of the history and motivation will occur in the colloquium talk and
this talk will emphasize ideas of proofs of the following theorem.  
Let G be a cocompact lattice in SL(n,R) where n>3, M a compact manifold
and a: G---> Diff(M) a homomorphism.  If dim(M)<n-1, a(G) is finite.
Furthermore if dim(M)=n-1 and a(G) preserves a volume form, a(G) is finite.  
The proof  has many surprising features, including that it uses hyperbolic
dynamics to prove an essentially elliptic result and that it uses results
on homogeneous dynamics,  including Ratner's measure classification theorem,
to prove results about inhomogeneous  system. If time permits I will say
a few words about the difficulties that arise when G is not cocompact.
This is joint work with Aaron Brown and Sebastian Hurtado.







SPECIAL ANNOUNCEMENT - COLLOQUIUM TALK:


20.05.2019, 14:10 (Monday) David Fisher (Indiana University, Bloomington, USA) - TIDY Distinguished Lecture



Title: Recent Progress on Zimmer's Conjecture
Location: Schreiber bldg., room 6, Tel-Aviv University



Abstract: Lattices in higher rank simple Lie groups are known to be extremely
rigid.  Examples of this are Margulis' superrigidity theorem, which
shows they have very few linear represenations, and Margulis'
arithmeticity theorem, which shows they are all constructed via number
theory.   Motivated by these and other results, in 1983 Zimmer made a
number of conjectures about actions of these groups on compact
manifolds.  After  providing some history and motivation, I will discuss
a very recent result, proving many cases of the main conjecture. While
avoiding  technical matters, I will try to describe some of the novel
flavor of the proof. The proof has many surprising features bringing
together  ideas from homogeneous dynamics, hyperbolic dynamics and
functional analyis. This is joint work with Aaron Brown and Sebastian Hurtado.








28.05.2019, 13:10 (Tuesday) Gang Tian  (Peking University, Princeton University) - Blumenthal Lecture in Geometry



SPECIAL LECTURE - PLEASE NOTE
THE DATE, PLACE & TIME





Title: TBA
Location: Orenstein bldg., room 110, 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) - Sackler Distinguished Lecture



Title: TBA

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



Abstract: TBA
















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