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

Location:  Schreiber bldg., room 309, TelAviv 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, TelAviv University  
Abstract:  Consider a polygonshaped 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, TelAviv 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, TelAviv University  
Abstract:  We
consider several constructions of quasimorphisms on the Hamiltonian
group of surfaces that were proposed by GambaudoGhys, 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, TelAviv University  
Abstract:  We will discuss connections between Gromov's work on isoperimetry of waists and Milman's work on the Mellipsoid of a convex body. It is proven that any convex body K in an ndimensional 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 (nd)dimensional volume is at least c^{nd}, 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, TelAviv 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 wellknown 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, TelAviv 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, TelAviv 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 biLipschitz invariant  
Location:  Schreiber bldg., room 309, TelAviv University  
Abstract:  Zariski has conjectured that multiplicity of a singularity of a hypersurface is a homeomorphism invariant. This conjecture is still unknown. However, a biLipschitz version of Zariski conjecture is true: multiplicity of biLipschitz hypersurface singularities is equal (Comte). The same is also true for surface singuarities (NewmannPichon). It was conjectured that the multiplicity is a biLipschitz invariant for singularity of any codimension. Using classification of 5manifolds, I would explain how to construct biLipschitz 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 WeilPetersson metric  
Location:  Schreiber bldg., room 309, TelAviv University  
Abstract:  I will begin this talk by recalling the classical WeilPetersson metric on Teichmüller space. McMullen showed that the WeilPetersson 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 WeilPetersson metric on the main cardioid of the Mandelbrot set. In my PhD thesis, I studied the WeilPetersson 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 DeligneMumford 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 HamiltonJacobi equation. A toy model: distance to a closed subset. 

Location:  Schreiber bldg., room 309, TelAviv University  
Abstract:  ABSTRACT  
02.01.2019, 14:1015:00 (Wednesday) 
Egor Shelukhin (University of Montreal)  
Title:  Upper bounds on the Lagrangian spectral norm  
Location:  Schreiber bldg., room 309, TelAviv 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, 15:1016:00 (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, TelAviv 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, TelAviv University  
Abstract:  In this talk I will discuss the Hamiltonian dynamics on the fourdimensional 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 nonchaotic properties. 

27.02.2019, 14:10 (Wednesday)  TBA  
Title:  TBA  
Location:  Schreiber bldg., room 309, TelAviv University  
Abstract:  TBA  
06.03.2019, 14:10 (Wednesday)  TBA  
Title:  TBA  
Location:  Schreiber bldg., room 309, TelAviv University  
Abstract:  TBA  
13.03.2019, 14:10 (Wednesday)  Marcelo Alves (ULB Brussels)  
Title:  TBA  
Location:  Schreiber bldg., room309, TelAviv University  
Abstract:  TBA  
20.03.2019, 14:10 (Wednesday)  TBA  
Title:  TBA  
Location:  Schreiber bldg., room 309, TelAviv University  
Abstract:  TBA  
27.03.2019, 14:10 (Wednesday)  TBA  
Title:  TBA  
Location:  Schreiber bldg., room 309, TelAviv
University  
Abstract:  TBA  
03.04.2019, 14:10 (Wednesday)  TBA  
Title:  TBA  
Location:  Schreiber bldg., room 309, TelAviv University  
Abstract:  TBA  
10.04.2019, 14:10 (Wednesday)  TBA  
Title:  TBA  
Location:  Schreiber bldg., room 309, TelAviv University  
Abstract:  TBA  
17.04.2019, 14:10 (Wednesday)  TBA  
Title:  TBA  
Location:  Schreiber bldg., room 309, TelAviv University  
Abstract:  TBA  
01.05.2019, 14:10 (Wednesday)  TBA  
Title:  TBA  
Location:  Schreiber bldg., room 309, TelAviv University  
Abstract:  TBA  
Conference: C^0 aspects of symplectic geometry and Hamiltonian dynamics, May 1216. 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, TelAviv 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, TelAviv University  
Abstract:  TBA  
05.06.2019, 14:10 (Wednesday)  Gerhard Knieper (RuhrUniversitat Bochum)  TIDY Distinguished Lecture  
Title:  TBA  
Location:  Schreiber bldg., room 309, TelAviv
University 

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

Location:  Schreiber bldg., room 309, TelAviv University  
Abstract:  TBA 
