Geometry & Dynamics Seminar 2011-12


 



 


13.06.2012, 12:10 (Wednesday) 

This is the second talk of the annual Blumenthal Lectures in Geometry.
Paul Biran (ETH) 


Title: Geometric & Algebraic Aspects of Lagrangian Topology and Organizational Matters

Location: Schreiber bldg., room 210, Tel-Aviv University


Abstract: Abstract




05.06.2012, 15:00 (Tuesday)

Joint Real & Complex Geometry - Geometry & Dynamics seminar
Michael Bialy, Tel Aviv University


Title: Hopf rigidity for convex billiards on Hemisphere and Hyperbolic plane

Location: Schreiber bldg., room 210, Tel-Aviv University


Abstract: Billiard ball motion inside a convex domain on constant curvature surface will be discussed.
I shall prove that the only billiards with no conjugate points are circular billiards.
This result has an important corollary saying that the only billiard ball maps which are "totally"
integrable are of circular billiards. Proof of these results relies on isoperimetric inequality on the surface.
No auxiliary knowledge is required.





19.03.2012, 17:00 (Monday)
Yoel Groman   (Hebrew University)  


Title: A reverse isoperimetric inequality for holomorphic curves

Location: Schreiber bldg., room 210, Tel-Aviv University 


Abstract: Let u be a J-holomorphic map from a compact Riemann surface with boundary
to a symplectic manifold such that the boundary is mapped into a Lagrangian submanifold.
Under natural assumptions on the target space we present an a priori linear bound on the
length of the boundary of u in terms of the area of u.  This can be seen as a generalization
of a classical result bounding the length of a real algebraic curve in terms of its degree.
The bound is important for defining open Gromov Witten invariants. We will discuss these
invariants and the role of the bound in their definition. This is joint work with Jake Solomon.   




16.11.2011, 13:00 (Wednesday)  Oleg Mokhov (Moscow University)


Title:
Hamiltonian and bi-Hamiltonian structures of hydrodynamic type
Location:
Schreiber bldg., room 209, Tel-Aviv University 




30.11.2011, 13:00 (Wednesday)  

Dmitry  Faifman (Tel-Aviv University)



Title:
Extending Schaffer's dual girth theorem to higher grassmannians

Location: Shenkar Physics Building, Room 211  Tel-Aviv University


Abstract: A theorem of Alvarez-Paiva (06'), conjectured (in a weak form) by Schaffer, states that the
length spectrum of a sphere of a normed space coincides with the length spectrum of the dual sphere.
We will extend this theorem to higher grassmannians, equipped with a natural Finsler structure
associated to a norm on the space of linear operators on the underlying space. The momentum map
associated with the action of the general linear group on the cotangent bundle will play a crucial role.




30.11.2011, 12:00 (Wednesday)   Sergei Lanzat (The Technion)


Title: Quasi-morphisms and quasi-states for non-closed symplectic manifolds
Location: Shenkar Physics Building, Room 211  Tel-Aviv University


Abstract: Previous results of Entov and Polterovich show that groups of symplectic diffeomorphisms of certain
closed symplectic manifolds (e.g. complex projective spaces) admit remarkable real-valued
”almost homomorphisms”, which also give rise to certain ”almost linear” real-valued functionals on
the space of continuous functions on the manifold. These objects, whose construction involves quantum
and Floer homology, have many interesting applications in symplectic topology. In this talk we will
discuss an analogous construction for non-closed symplectic manifolds and its applications.




21.12.2011, 13:30 (Wednesday)   Leonid Polterovich (Tel-Aviv University and University of Chicago)


Title: Quantum noise and symplectic rigidity
Location: Amado 814, The Technion


Abstract: We discuss a link between "hard" symplectic topology and an unsharpness
principle for generalized quantum observables (positive operator valued measures).
The link is provided by the Berezin-Toeplitz quantization.








Organized by Michael Bialy, Michael Entov, & Yaron Ostrover