Geometry & Dynamics Seminar 2015-16

In the 2nd semester the seminar will take place in Schreiber Building room 309, on Wednesdays at 14:10.

Please check each announcement since this is sometimes changed.

21.10.2015, 14:10 (Wednesday)	Asaf Kislev (Tel Aviv University)
Title:	Geometry of general relativity
Location:	Schreiber bldg., room 209, Tel-Aviv University
Abstract:	We will see the mathematical framework of general relativty, and describe the predictions of general relativity regarding light deflection, and time dilation.
28.10.2015, 14:10 (Wednesday)	Matthias Meiwes (Universität Münster)
Title:	Leafwise Intersections on Hypertight Contact Manifolds
Location:	Schreiber bldg., room 209, Tel-Aviv University
Abstract:	Abstract
4.11.2015, 14:10 (Wednesday)	Albert Fathi (École Normale Supérieure de Lyon)
Title:	A Urysohn type theorem under a dynamical constraint
Location:	Schreiber bldg., room 007, Tel-Aviv University
Abstract:	Abstract
11.11.2015, 14:10 (Wednesday)	Shmuel Weinberger (University of Chicago) - MINT Distinguished Lecture
Title:	Topological Problems of Data Analysis
Location:	Schreiber bldg., room 007, Tel-Aviv University
Abstract:	Dealing with large and multidimensional data is a ubiquitous problem in many scientific and financial settings. In recent years, geometric and topological methods have become increasingly popular. They suggest problems that are at the interface of probability, differential geometry, topology, and analysis. The first lecture will be devoted to an overview of these ideas, while the second will focus on some topological problems that arise in trying to make some heuristics rigorous and/or practical.
18.11.2015, 14:10 (Wednesday)	Jake Solomon (Hebrew University)
Title:	The degenerate special Lagrangian equation
Location:	Schreiber bldg., room 007, Tel-Aviv University
Abstract:	A Lagrangian L in a Calabi-Yau manifold is called positive if the real part of the holomorphic volume restricted to L is positive. The degenerate special Lagrangian equation governs geodesics in the space of positive Lagrangians. The existence of a geodesic between two positive Lagrangians implies a lower bound on the cardinality of their intersection related to the strong Arnold conjecture. I will explain some recent results on existence and uniqueness in the case of graph Lagrangians in C^n. This is joint work with Y. Rubinstein.
25.11.2015, 14:10 (Wednesday)	NO SEMINAR THIS WEEK!
2.12.2015, 14:10 (Wednesday)	Bo Berndtsson (Chalmers University of Technology) (Blumenthal Lecture in Geometry)
Title:	Complex Brunn-Minkowski Theory
Location:	Schreiber bldg., room 007, Tel-Aviv University
Abstract:	Abstract
09.12.2015, 14:10 (Wednesday)	Sara Tukachinsky (Hebrew University)
Title:	The Maurer-Cartan equation and Gromov-Witten theory
Location:	Schreiber bldg., room 007, Tel-Aviv University
Abstract:	Dealing with pseudo-holomorphic disks, $A_\infty$-algebras supply a convenient working language. In particular, solutions to the Maurer-Cartan equation, a.k.a. bounding chains, allow us to describe bubbling at the boundary. Such bubbling is an obstacle for defining structures related to Lagrangians, such as Floer cohomology or open Gromov-Witten invariants. In my talk I will define, following Fukaya's approach, an $A-\infty$ structure on the ring of differential forms on a Lagrangian, and explain the suitable Maurer-Cartan equation. Depending on time constraints, I will talk about applications to Floer theory [Fukaya et al.] and/or the use of bounding chains in defining open Gromov-Witten invariants, i.e., invariants that count pseudo-holomorphic disks that satisfy given constraints [joint work with Jake Solomon]. These invariants fit in a family of equations, named WDVV equations, that tie them with a quantum product on relative cohomology. No previous knowledge of any of the objects mentioned above will be assumed.
16.12.2015, 14:10 (Wednesday)	Arseniy Akopyan (IST Austria).
Title:	Circle patterns and confocal conics
Location:	Schreiber bldg., room 007, Tel-Aviv University
Abstract:	We construct some circle patterns which is naturally related with conics and quadrics in space. Our main new results are on checkerboard circumscribed nets in the plane and in spaces of higher dimension. We show how this larger class of this nets appears quite naturally in Laguerre geometry of oriented planes and spheres and leads to new remarkable incidence theorems joint work with Alexander Bobenko.
16.12.2015, 15:10 (Wednesday)	Roman Karasev (Moscow Institute of Physics and Technology).
Title:	Bezdek--Bezdek approach to billiards and symplectic capacities
Location:	Schreiber bldg., room 007, Tel-Aviv University
Abstract:	We will discuss the approach of K. Bezdek and D. Bezdek to characterizing the minimal length of a closed billiard trajectory in a convex body as minimum of lengths of closed polygonal lines under a certain constraint. This approach allows useful extensions to arbitrary non-symmetric norm, with which the length is measured, and to possibly non-smooth bodies, eventually giving a practical tool to calculate the Ekeland--Hofer--Zehnder capacity of convex Lagrangian products. Some examples of such calculations will be given.
23.12.2015, 14:10 (Wednesday)	Yasha Eliashberg (Stanford University) (Sackler distinguished lecture)
Title:	Renaissance of the h-principle in symplectic topology
Location:	Schreiber bldg., room 007, Tel-Aviv University
Abstract:	In  geometry and topology, as well as in applications of Mathematics to Physics and other areas, one often deals with systems of partial differential equations and inequalities. By replacing derivatives of unknown functions by independent functions one gets a system of algebraic equations and inequalities. The solvability of this algebraic system is necessary for the solvability of the original system of differential equations. It was a surprising discovery in the 1950-60s that there are geometrically interesting classes of systems for which this necessary condition is also sufficient. This led to counter-intuitive results, like Steven Smale’s famous inside-out “eversion” of the 2-sphere and John Nash’s isometric embedding of the unit sphere into a ball of an arbitrary small radius. Many more instances of this phenomenon, called by Mikhail Gromov h-principle (“h” stands for homotopy), were since then found and continue to be discovered, most recently in symplectic topology. In the first lecture I will describe the main ideas and classical methods and results of the h-principle, and in the second I will discuss recent breakthroughs on the flexible side of symplectic topology.
30.12.2015, 14:10 (Wednesday)	Egor Shelukhin  (Institute for Advanced Study, Princeton)
Title:	Lagrangian cobordisms and metric invariants
Location:	Schreiber bldg., room 007, Tel-Aviv University
Abstract:	The notion of a cobordism between two submanifolds of a given manifold admits an interesting parallel in the world of Lagrangian submanifolds of a symplectic manifold. We describe various natural ways of measuring the distance between two (possibly non-isotopic!) Lagrangian submanifolds based on this notion of cobordism (and its extensive Floer-theoretic investigation by Biran and Cornea), and study the non-degeneracy and degeneracy properties of the resulting pseudo-metrics. This is a joint work with Octav Cornea.
6.1.2016, 14:10 (Wednesday)	Tadashi Tokieda (Cambridge), TIDY distinguished lecture
Title:	Science from a sheet of paper
Location:	Schreiber bldg., room 007, Tel-Aviv University
24.2.2016, 14:10 (Wednesday)	Stepan Orevkov (Université Paul Sabatier, Toulouse)
Title:	On algebraic knots and links in RP^3
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	We study connected components of the set of nonsingular real algebraic curves in RP^3 of given degree and genus (also called rigid isotopy classes of such curves). We give a complete classification of up to degree 6. It happens that in this case, the rigid isotopy type is determined by the usual isotopy type and the so called encomplexed writhe (an invariant introduced by Viro). For any degree d we show that there is a unique rigid isotopy class realizing the maximal value of the encomlexed writhe for rational curves: the class of a curve of bidegree (d-1,1) on a hyperboloid.
02.3.2016, 14:10 (Wednesday)	Anton Petrunin (Pennsylvania State University)
Title:	Invitation to Alexandrov geometry, curvature bounded above.
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	An introductory-survey which discuss the definitions of CAT(0) spaces and the applications including construction of exotic compact aspherical manifolds and estimate of number of collisions of hard-ball in the Euclidean space. (These are results of Davis and  Burago--Ferleger--Kononenko)
09.03.2016, 14:10 (Wednesday)	Cedric Membrez (TAU)
Title:	pb_4^+ invariants and Lagrangian topology
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	After a short introduction to pb_4^+ invariants we apply them to Lagrangian topology. We describe methods for computing these invariants in the case of Lagrangian tori and provide examples. This is joint work with Michael Entov, Yaniv Ganor and Leonid Polterovich.
16.03.2016, 14:10 (Wednesday)	Frol Zapolosky (Haifa University)
Title:	Spectral invariants for contactomorphisms of monotone prequantization bundles and applications
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	I'll sketch the construction of a Floer homology theory for  prequantization spaces over monotone symplectic manifolds and of the  spectral invariants resulting therefrom. I'll present a few  applications among which a Floer-theoretic construction of a  quasi-morphism on the universal cover of Cont_0 of the standard real  projective spaces, whose pullback to the Hamiltonian group of the  underlying complex projective spaces coincides with the Entov-Polterovich  Calabi quasi-morphism. This is joint work in progress with Peter Albers and Egor Shelukhin.
23.03.2016, 14:10 (Wednesday)	Jarek Kedra (University of Aberdeen)
Title:	Uniformly bounded groups
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	A group G is called bounded if every conjugation invariant norm on G has bounded diameter. I will introduce the notion of a uniformly bouned group which is a stronger than that of a bounded group and generalises the concept of a uniformly simple group. I will discuss examples: Lie groups, lattices in Lie groups, diffeomorphism groups. As an application I will recover Delzant's theorem that semisimple Lie groups without compact factors don't admit Hamiltonian actions on symplectic manifolds. This is a joint work (in progress) with Assaf Libman.
30.03.2016, 14:10 (Wednesday)	Lara Simone Suárez (HUJI)
Title:	Exact Lagrangian cobordism and pseudo-isotopy
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	Consider two Lagrangian submanifolds $L$, $L'$ in a symplectic manifold $(M, \omega)$. A Lagrangian cobordism $(W; L, L')$ is a smooth cobordism between $L$ and $L'$ admitting a Lagrangian embedding in $(([0,1]\times \mathbb{R}) \times M, (dx\wedge dy) \oplus \omega)$ that looks like $[0, \epsilon) \times \{1\} \times L$ and $(1- \epsilon, 1] \times \{1\} \times L'$ near the boundary. In this talk we will show that under some topological constrains, an exact Lagrangian cobordism $(W; L, L')$ with $dim(W) > 5$ is diffeomorphic to $[0,1] \times L$.
06.04.2016, 14:10 (Wednesday)	Michael Brandenbursky (BGU)
Title:	L^p-metrics, palindromes and autonomous flows
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	I will discuss a number of results on the interrelation between the L^p -metric on the group of Hamiltonian diffeomorphisms of surfaces and the subset A of autonomous Hamiltonian diffeomorphisms. In particular, I will show that there are Hamiltonian diffeomorphisms of all surfaces of genus g ≥ 2 or g = 0 lying arbitrarily L^p -far from the subset A, answering a variant of a question of Polterovich for the L^p -metric. In addition, I will discuss a relation between palindromes on a free group and autonomous metric on the group of Hamiltonian diffeomorphisms of a torus.
06.04.2016, 15:10 (Wednesday)	Alexey Bolsinov (Loughborough University)
Title:	Stability analysis and singularities of bi-Hamiltonian systems
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	In the theory of integrable systems, there are two popular topics: 1) Topology of integrable systems, which studies stability of equilibria and periodic trajectories, bifurcations of Liouville tori, singularities and their invariants, topological obstructions to the integrability and so on. 2) Theory of compatible Poisson brackets, which studies one of the most interesting  mechanisms of integrability based on the existence of a bi-Hamiltonian representation. The aim of the talk is to to construct a bridge between these two areas and to explain how singularities of bi-Hamiltonian systems are related to algebraic properties of compatible Poisson brackets. This bridge provides new stability analysis methods for a wide class of integrable systems.
13.04.2016, 14:10 (Wednesday)	Lev Buhovski (TAU)
Title:	C^0 Hamiltonian dynamics and the Arnold conjecture
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	After introducing Hamiltonian homeomorphisms and recalling some of their properties, I will focus on fixed point theory for this class of homeomorphisms. The main goal of this talk is to present the outlines of a C^0 counter example to the Arnold conjecture in dimensions higher than two. This is joint work with Vincent Humiliere and Sobhan Seyfaddini
20.04.2016, 14:10 (Wednesday)	Alexander I. Esterov  (National Research University Higher School of Economics, Moscow)
Title:	Abel-Ruffini theorem for systems of equations
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	The classical Abel-Ruffini theorem claims that the general polynomial equation of degree d is solvable in radicals iff d does not exceed 4. I will present an analogue of this theorem for systems of equations: the square system of general polynomial equations with the Newton polytope N is solvable in radicals iff it has at most 4 solutions, i.e. the integer volume of N is at most 4. This in particular allows to classify all solvable systems. The only known proof involves recent strong results on Newton polytopes and on finite groups. The same question for a system of equations with non-equal Newton polytopes of equations is an open problem.
04.05.2016, 14:10 (Wednesday)	Egor Shelukhin (Institute for Advanced Study, Princeton)
Title:	Non-trivial Hamiltonian fibrations via K-theory quantization
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	We show how family quantization with values in K-theory can detect non-trivial Hamiltonian fibrations, and give examples of such fibrations that are not detected by previous methods (the characteristic classes of Reznikov for example). We further discuss related results. Joint work with Yasha Savelyev.
25.05.2016, 14:10 (Wednesday)	Igor Uljarevic ( ETH-Zurich)
Title:	A symplectic homology theory for automorphisms of Liouville domains
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	We introduce a combination of fixed point Floer homology and symplectic homology for Liouville domains. As an application, we detect non-trivial symplectic mapping classes of a Liouville domain.
25.05.2016, 15:10 (Wednesday)	Michael Khanevsky (Brussels)
Title:	Quasimorphisms on the Hamiltonian groups of surfaces and the Hofer metric
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	There are several constructions of quasimorphisms on the Hamiltonian groups  of surfaces that were proposed by Gambaudo-Ghys, Polterovich, Py, etc. These constructions are based on topological invariants either of individual orbits or of orbits of finite configurations of points and the quasimorphism computes the average value of these invariants along the surface. We show that many quasimorphisms that arise this way are not Hofer continuous. This allows to show non-equivalence of Hofer's metric and some other metrics on the Hamiltonian group.
01.06.2016, 14:10 (Wednesday)	Yoshihiro Sugimoto (Kyoto)
Title:	Hofer's metric and wrapped Floer homology
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	In this talk, I will explain a relationship between displaceability and vanishing of wrapped Floer homology. This argument can be used to prove vanishing of symplectic homology. I also explain an application of this relationship to the Hofer's metric of the space of Lagrangian submanifolds.
01.06.2016, 15:10 (Wednesday)	Suguru Ishikawa (Kyoto)
Title:	An estimate of spectral invariant and non-displaceability
Location:	Schreiber bldg., room 309, Tel-Aviv University
Abstract:	Entov and Polterovich introduced the notion of a (super)heavy subset of a symplectic manifold by using spectral invariants of Floer homology. Superheavy set cannot be displaced by symplectic isotopy, and heavy set cannot be displaced by Hamiltonian isotopy. Since (super)heavyness is preserved by product, one example of (super)heavy set gives us a lot of examples of non-displaceable subsets. We found new kind of superheavy sets by direct calculations of spectral invariants of distance-like Hamiltonians. We showed if convex open subsets in Euclidian space are disjointly embedded in a spherically negative monotone closed symplectic manifold, their compliment is superheavy. The key of the proof is estimates of the Conley-Zehnder index of periodic orbits of distance-like HamiltonianA