Geometry & Dynamics Seminar 2016-17

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

Please check each announcement since this is sometimes changed.

02.11.2016, 14:10 (Wednesday)	Orientation meeting for students
Location:	Schreiber bldg., room 309, Tel-Aviv University
09.11.2016, 14:10 (Wednesday)	Dmitri Burago (Penn State)
Title:	A few fairy Math tales
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	Abstract
16.11.2016, 14:10 (Wednesday)	Nir Lev (BIU)
Title:	Equidistribution estimates for Fekete points on complex manifolds
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	I will discuss extremal point configurations, called Fekete points, on a compact complex manifold. Their equidistribution is a result due to Berman, Boucksom and Witt Nystrom. We propose another approach to the result based on the relation of Fekete points to another array of points, the sampling and interpolation points. This approach allows us to estimate the equidistribution of the Fekete points quantitatively. Joint work with Joaquim Ortega-Cerda.
23.11.2016, 14:10 (Wednesday)	Dong Chen (Penn State)
Title:	Two types of KAM-nondegenerate nearly integrable systems with positive metric entropy
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	The celebrated KAM theory says that if one makes a small perturbation of  a non-degenerate completely integrable system, we still have a huge measure  of invariant tori with quasi-periodic dynamics in the perturbed system. These invariant tori are known as KAM tori. What happens outside KAM tori draws lots of attention. In this talk I will present two types of C^\infty small Lagrangian perturbation of the geodesic flow on a flat torus. Both resulting flows have positive metric entropy, from which we get positive metric entropy outside some KAM tori. What is special in the second type is that positive metric entropy comes from an arbitrarily small tubular neighborhood of one trajectory. This is a joint work with D. Burago and S. Ivanov.
30.11.2016, 14:10 (Wednesday)	Liat Kessler (Univesity of Haifa at Oranim)
Title:	Extending Homologically trivial symplectic cyclic actions to Hamiltonian circle actions
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	We ask whether every homologically trivial cyclic action on a symplectic four-manifold extend to a Hamiltonian circle action. By a cyclic action we mean an action of a cyclic group of finite order; it is homologically trivial if it induces the identity map on homology. We assume that the manifold is closed and connected. In the talk, I will give an example of a homologically  trivial symplectic cyclic action on a four-manifold that admits Hamiltonian circle actions, and show that is does not extend to a Hamiltonian circle action. I will also discuss symplectic four-manifolds on which every homologically trivial cyclic action extends to a Hamiltonian circle action. I will deduce corollaries on the existence of homologically trivial cyclic actions and on embedding finite-order cyclic subgroups of the group of Hamiltonian symplectomorphisms  in circle subgroups. This work applies holomorphic methods to extend combinatorial tools developed for circle actions to study cyclic actions.
7.12.2016, 14:10 (Wednesday)	Tali Pinsky (TIFR, India)
Title:	On the Lorenz flow and the modular surface
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	The talk addresses three famous, albeit fundamentally different, three dimensional flows: The geodesic flow on the modular surface, the chaotic Lorenz equations and the geometric Lorenz model. I will describe a new approach showing that, surprisingly, these flows  are essentially orbit equivalent for the correct choice of parameters. This will be an introductory talk.
14.12.2016, 14:10 (Wednesday)	Nikolai Nadirashvili (Aix-Marseille Université, CNRS) - MINT Distinguished Lecture
Title:	Geometry of trajectories to Euler Equation and level sets of solutions to elliptic equations
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	We discuss Liouville theorems and some geometric properties of stationary flows of the ideal fluid in dimensions 2 and 3.
21.12.2016, 14:10-15:00 (Wednesday)	Junyoung Lee (TAU)
Title:	Regularization of Hill’s lunar problem and its systole bound
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	We discuss Moser regularization of celestial mechanics problems and some symplectic results on the regularized problems. Using Floer theory, we can obtain information about periodic orbits. In particular, this result will give a systole bound for Hill’s lunar problem.
21.12.2016, 15:10-16:00 (Wednesday)	Boris Khesin (U. of Toronto)
Title:	Invariants of functions on symplectic surfaces and ideal hydrodynamics
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	We describe a classification of simple Morse functions on symplectic surfaces with respect to actions of symplectomorphism groups. We also describe generic coadjoint orbits and Casimirs for such groups. This gives an answer to V.Arnold's problem on describing all invariants of generic isovorticed fields for the 2D ideal incompressible fluids. For this we introduce a notion of anti-derivatives on a measured Reeb graph and describe their properties. This is a joint work with Anton Izosimov and Mehdi Mousavi.
28.12.2016, 14:10-15:00 (Wednesday)	David Fajman  (University of Vienna)
Title:	Dynamics of Spacetime — Einstein’s equations as a geometric flow
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	The interpretation of Einstein’s equations as a geometric flow (the Einstein flow)  allows to study the evolution of spacetimes from a dynamical point of view. Two types of initial data are mainly considered: Firstly, asymptotically flat  data describing initial states of isolated self-gravitating systems and secondly,  data on closed manifolds describing initial states for cosmological spacetimes.  Studying the evolution of data under the flow we aim to understand its long-time  behavior and the global geometry of its time-development. We are interested in  the construction of static solutions (or static up to a time-rescaling) as potential  attractors of the flow and their nonlinear stability, completeness and incompleteness  properties of spacetimes and singularity formation. We present new methods to  construct and study solutions by geometric and analytical tools as well as several  results in the directions mentioned above. We consider in particular the case of  matter models coupled to the Einstein equations, which turns out to provide several  interesting phenomena and new classes of solutions.
28.12.2016, 15:10-16:00 (Wednesday)	Albert Fathi (Ecole normale supérieure de Lyon, France)
Title:	Topology of the set of singularities of viscosity solutions of the Hamilton-Jacobi equation
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	This is a joint work with Piermarco Cannarsa and Wei Cheng. We study the properties of the set S of non-differentiable points of viscosity solutions of the Hamilton-Jacobi equation, for a Tonelli Hamiltonian. The main surprise is the fact that this set is locally arc connected—it is even locally contractible. This last property is far from generic in the class of semi-concave functions. We also “identify” the connected components of this set S. This work relies on the idea of Cannarsa and Cheng to use the positive Lax-Oleinik operator to construct a global propagation of singularities (without necessarily obtaining uniqueness of the propagation).
04.01.2017, 14:10 (Wednesday)	Yair Minsky (Yale University) (Blumenthal Lecture in Geometry)
Title:	Fibrations, subsurface projections and veering triangulations
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	When a hyperbolic 3-manifold fibers over the circle, its geometric features can be read from the fine structure of its monodromy map, specifically the "subsurface projections" of the stable and unstable foliations to the arc complexes of subsurfaces of the fiber. While this correspondence is useful when the topological type of the fiber is fixed, it is not well-understood in general. A good laboratory for studying this is a single 3-manifold that fibers in infinitely many different ways, as organized by Thurston's norm on homology. In this setting there are canonical triangulations due to Agol, which can be studied very explicitly via a construction of Gueritaud. We explore how the subsurface projections of monodromies for all the fibers can be seen in the structure of this triangulation, and how this leads to a nice combinatorial picture with estimates that do not depend on complexity of the fibers. Joint work with Sam Taylor.
11.01.2017, 14:10 (Wednesday)	Paul Biran (ETH) - MINT Distinguished Lecture
Title:	It takes Energy to Split Lagrangians
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	We will discuss a Hofer Geometry analog that naturally arises from Lagrangian cobordism theory, and see how it can be used to measure relations between Lagrangian submanifolds.
18.1.2017, 14:00-15:50 (Wednesday)	Laszlo Babai (University of Chicago) - (Sackler Distinguished Lectures)
Title:	Finite Permutation Groups And The Graph Isomorphism Problem
Location:	Melamed Hall (6), Shenkar Physics building, Tel-Aviv University
Abstract:	Abstract
25.1.2017, 14:10 (Wednesday)	No Seminar This Week!
Title:	No Seminar This Week!
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	TBA
15.3.2017, 14:10 (Wednesday)	Iosif Polterovich (Université de Montréal)
Title:	Sloshing, Steklov and corners
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	The sloshing problem is a Steklov type eigenvalue problem describing small oscillations of an ideal fluid. We will give an overview of some latest advances in the study of Steklov and sloshing spectral asymptotics, highlighting the effects arising from corners, which appear naturally in the context of sloshing. In particular, we will outline an approach towards proving the conjectures posed by Fox and Kuttler back in 1983 on the asymptotics of sloshing frequencies in two dimensions. The talk is based on a joint work in progress with M. Levitin, L. Parnovski and D. Sher.
22.3.2017, 14:10 (Wednesday)	Semyon Alesker (TAU)
Title:	Some conjectures on intrinsic volumes on Riemannian and Alexandrov spaces.
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	Hadwiger's theorem says that linear combinations of intrinsic volumes on convex sets are the only isometry invariant continuous valuations (= finitely additive measures). On the other hand H. Weyl has extended intrinsic volumes beyond convexity, to Riemannian manifolds. We try to understand the continuity properties of this extension under the Gromov-Hausdorff convergence (literally, there is no such continuity in general). First, we describe a new conjectural compactification of the set of all closed Riemannian manifolds with given upper bounds on dimension and diameter and lower bound on sectional curvature. Points of this compactification are pairs: an Alexandrov space and a constructible (in the Perelman-Petrunin sense) function on it. Second, conjecturally all intrinsic volumes extend by continuity to this compactification. No preliminary knowledge of Alexandrov spaces will be assumed, though it will be useful.
29.03.2017, 14:10 (Wednesday)	Carlos Kenig (University of Chicago)  - MINT Distinguished Lecture
Title:	The energy critical wave equation: soliton decomposition along well chosen sequences of time in the non-radial case.
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	We will discuss the recent work of Duyckaerts-Jia-Kenig-Merle establishing soliton resolution along well chosen sequences of times converging to the final time of existence, for non-radial solutions of the energy critical nonlinear wave equation which remain bounded in the energy space.
05.04.2017, 14:10 (Wednesday)	Jun Zhang (TAU)
Title:	Persistent homology in symplectic topology
Location:	Schreiber bldg., room 006, Tel-Aviv University (NOTE THE UNUSUAL LOCATION!)
Abstract:	In this talk, I will first briefly explain (a joint work with M. Usher) how to modify the classical persistent homology to be defined directly on the chain complex level in the sense that we also have decomposition theorem, stability theorem and well-defined barcode. Then I will demonstrate an application of this construction by improving the main result from L. Polterovich and E. Shelukhin’s recent work on Hofer distance between autonomous Hamiltonian diffeomorphisms and time-dependent ones. Finally, I will mention some other types of persistence modules or possible applications of persistent homology in contact topology.
19.04.2017, 14:10 (Wednesday)	David Levin (TAU)
Title:	Attractors of Sequences of Function Systems, and the relation to Non-Stationary Subdivision
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	Iterated Function Systems (IFS) have been at the heart of fractal geometry almost from its origin. Subdivision schemes are widely used in computer graphics. Several attempts have been made to link limits generated by subdivision schemes to fractals generated by iterated function systems. With an eye towards establishing connection between non-stationary subdivision schemes and fractals, this talk introduces the notion of "trajectories of maps defined by function systems" which may be considered as a new generalization of the traditional IFS. The significance and the convergence properties of 'forward' and 'backward' trajectories is presented. Unlike the ordinary fractals which are self-similar at different scales, the attractors of these trajectories may have different structures at different scales.
26.04.2017, 14:10 (Wednesday)	Alexander P. Veselov (Loughborough University)
Title:	Deligne-Mumford moduli spaces, integrable tops and separation of variables
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	I will explain the relation between integrable N-dimensional tops and the real version of Deligne-Mumford moduli space of stable genus zero curves with N+1 marked points. The known results about geometry of this space and combinatorics of closely related Stasheff polytope will be applied to the classification of separation variables on a sphere. The talk is a review of joint results with Aguirre, Felder and Schoebel.
26.04.2017, 15:10 (Wednesday)	Alfonso Sorrentino (Università degli Studi di Roma “Tor Vergata”)
Title:	Spectral properties and integrability of Birkhoff billiards
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	A mathematical billiard is a system describing the inertial motion of a point mass inside a domain, with elastic reflections at the boundary. This simple model has been first proposed by G.D. Birkhoff as a mathematical playground where “the formal side, usually so formidable in dynamics, almost completely disappears and only the interesting qualitative questions need to be considered”. Since then billiards have captured much attention in many different contexts, becoming a very popular subject of investigation. Despite their apparently simple (local) dynamics, their qualitative dynamical properties are extremely non-local. This global influence on the dynamics translates into several intriguing rigidity phenomena, which are at the basis of several unanswered questions and conjectures. In this talk I shall focus on several of these questions. In particular, I shall  describe some recent results related to the possibility of inferring dynamical information on the billiard map, from its length spectrum (i.e., the collection of lengths of its periodic orbits), and on the classification of integrable billiards (also known as Birkhoff conjecture). This talk is based on joint works with G. Huang and V. Kaloshin.
03.05.2017 14:10 (Wednesday)	Igor Uljarevic (TAU)
Title:	Tamura's theorem via symplectic homology
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	In this talk, I will show how symplectic homology can be used to prove some non-obvious results about partitions of the set of positive integers.
10.05.2017, 14:10 (Wednesday)	Shira Tanny (TAU)
Title:	Bounding the Poisson bracket invariant on surfaces
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	I will discuss the Poisson bracket invariant of covers, which was initially introduced by L. Polterovich. The works of L. Polterovich, S. Seyfaddini and S. Ishikawa have studied this invariant via Floer theory, and lower bounds for it were established in some situations. I will explain how one can improve the known lower bounds in dimension 2, using only elementary arguments. This is a joint work with L. Buhovsky. We express our gratitude to F. Nazarov for his contribution to this work.
17.05.2017, 14:10 (Wednesday)	Henri Berestycki (EHESS, PSL Research University - Paris)
Title:	The dynamics and propagation of riots
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	In this talk, I report on a model aiming at studying the dynamics and spreading of riots. It involves an epidemiological approach for the dynamics with a diffusion interaction term. I will discuss this model in the setting of the French riots in 2005 and compare its outcome with a rather detailed set of data for these riots. I will also describe some mathematical results regarding a related dynamical system that is relevant in this context.
SPECIAL SEMINAR NOTE THE DATE, ROOM AND TIME! 22.05.2017, 11:10 (Monday)	Daniel Sternheimer (Department of Mathematics, Rikkyo University, Tokyo, Japan & Institut de Mathématiques de Bourgogne, Dijon, France)
Title:	Deformation Quantization, Genesis and Avatars: An introduction with some results and perspectives.
Location:	Orenstein bldg., room 102, Tel-Aviv University
Abstract:	In 1963/64 appeared both index theorems for (elliptic) pseudodifferential operators and Gerstenhaber’s theory of deformations of algebras. I participated then in the Paris seminar giving a proof of the first, and afterward used the second for physics. In the mid-seventies the two converged to explain quantum mechanics as a deformation of classical mechanics, using symplectic (or Poisson) geometry, what is now called ``deformation quantization”. Quantum groups and noncommutative geometry (which appeared in the early 80s in different contexts) can be considered as avatars of that approach. I shall explain in general terms what are these notions, and describe some results and perspectives. The talk should be of interest to mathematicians and open-minded theoretical physicists.
24.05.2017, 14:10 (Wednesday)	Rene Rühr (TAU)
Title:	Effective Counting on Translation Surfaces
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	I will explain an effective version of a result of Eskin and Masur: for any SL2(R)-invariant locus L of translation surfaces, there exists κ > 0, such that for almost every translation surface in L, the number of saddle connections with holonomy vector of length at most T, grows like cT^2 + O(T^{2−κ}). Here c > 0 is the Siegel-Veech constant associated with L. The talk will provide some definitions, some pictures and some history. Joint work with Amos Nevo and Barak Weiss.
07.06.2017, 14:10 (Wednesday)	Vadim Kaloshin (University of Maryland)- MINT Distinguished Lecture
Title:	Birkhoff Conjecture for convex planar billiards
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	G.D.Birkhoff introduced a mathematical billiard inside of a convex domain as the motion of a massless particle with elastic reflection at the boundary. A theorem of Poncelet says that the billiard inside an ellipse is integrable, in the sense that the neighborhood of the boundary is foliated by smooth closed curves and each billiard orbit near the boundary is tangent to one and only one such curve (in this particular case, a confocal ellipse). A famous conjecture by Birkhoff claims that ellipses are the only domains with this property. We show a local version of this conjecture - namely, that a small perturbation of an ellipse has this property only if it is itself an ellipse. This is based on several papers with Avila, De Simoi, G.Huang, Sorrentino.
14.06.2017, 14:10 (Wednesday)	Yael Karshon (University of Toronto)
Title:	Non-linear Maslov index on lens spaces
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	Let  L  be a lens space with its standard contact structure. We construct a "non-linear Maslov index", which associates an integer to any contact isotopy of  L,  and which gives a quasimorphism on the universal cover of the identity component of the contactomorphism group of  L. We use it to prove contact rigidity properties of L. This work is joint with Gustavo Granja, Milena Pabinia, and Sheila (Margherita) Sandon, and it follows earlier work of Givental and Theret that applied to real and complex projective spaces.
21.06.2017, 14:10 (Wednesday)	Semyon Alesker (TAU)
Title:	Calabi type problem for Monge-Ampere equations on HKT manifolds
Location:	Dan David bldg., room 106, Tel-Aviv University - NOTE THE SPECIAL ROOM!
Abstract:	Real and complex Monge-Ampere equations play a central role in several branches of geometry and analysis. We introduce  a quaternionic version of a Monge-Ampere equation which is an analogue of the famous Calabi problem in the complex case. It is a non-linear elliptic equation of second order on so called HyperKahler with Torsion (HKT) manifolds (the latter manifolds were introduced by physicists in 1990's). While in full generality it is still unsolved, we will describe its solution in a special case and some partial results towards its proof in the general case. Part of the results are joint with M. Verbitsky and E. Shelukhin.
05.07.2017, 14:10 (Wednesday)	Asaf Kislev  (TAU)
Title:	A quasi-isometric embedding into $Ham(M,\omega)$ -- based on a paper by Bret Stevenson
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	Let $f$ be a Hamiltonian diffeomorphism on a closed symplectic manifold $M$. The Hofer norm of $f$ is the minimal oscillation norm of a Hamiltonian function which generates $f$ as its time-1-map. We think about it as the minimal energy needed to generate the dynamics of $f$. This norm gives $Ham(M,\omega)$ a very interesting geometrical structure, and it has many applications in symplectic topology. There are many open questions about the geometry of $Ham(M,\omega)$, even when $M$ is a "simple" symplectic manifold like $S^2$. In this talk I will describe a construction by Bret Stevenson of a quasi-isometric embedding of $[0,1]^{\infty}$ into $Ham(M,\omega)$, where $M$ satisfies certain conditions. The construction relies on results related to barcodes associated to the filtered Floer homology of radially symmetric Hamiltonians.