Manchester Building (Hall 2), Hebrew University Jerusalem
Hamiltonian Floer cohomology was invented by A. Floer to prove the Arnold conjecture: a Hamiltonian diffemorphism of a closed symplectic manifold has at least as many periodic orbits as the sum of the Betti numbers. A variant called Symplectic cohomology was later defined for certain non compact manifolds, including the cotangent bundle of an arbitrary closed smooth manifold. The latter is the setting for classical mechanics of constrained systems. Read more about Colloquium: Yoel Groman (HUJI) - Floer homology of the magnetic cotangent bundle
Manchester Building (Hall 2), Hebrew University Jerusalem
Physical systems are regularly studied as spatial point sets, and so understanding the structure in such sets is a very natural problem. However, aside from several special cases, describing the manner in which a set of points can be arranged in space has been historically challenging. In the first part of this talk, I will show how consideration of the configuration space of local arrangements of neighbors, and a few simple results in metric geometry, can shed light on essential challenges of this problem, and in the classification of data more generally.
Manchester Building (Hall 2), Hebrew University Jerusalem
Title: Quantum footprints of symplectic rigidity
Abstract: I'll discuss an interaction between symplectic topology, a rapidly developing mathematical area originated as a geometric language for problems of classical mechanics, and quantum mechanics. On one hand, ideas from quantum mechanics give rise to new structures on the symplectic side, and quantum mechanical insights lead to useful symplectic predictions. On the other hand, some phenomena discovered within symplectic topology admit a translation into the language of quantum mechanics.
Manchester Building (Hall 2), Hebrew University Jerusalem
Title: Needle decomposition and Ricci curvature
Abstract: Needle decomposition is a technique in convex geometry,
which enables one to prove isoperimetric and spectral gap
inequalities, by reducing an n-dimensional problem to a 1-dimensional
one. This technique was promoted by Payne-Weinberger, Gromov-Milman
and Kannan-Lovasz-Simonovits. In this lecture we will explain what
needles are, what they are good for, and why the technique works under
lower bounds on the Ricci curvature.
Manchester Building (Hall 2), Hebrew University Jerusalem
Title: The (B)-conjecture andfunctional inequalities
Abstract:
The log-Brunn-Minkowski inequality is an open problem in convex geometry regarding the volume of convex bodies. The (B)-conjecture is an apparently different problem, originally asked by probabilists, which turned out to be intimately related the the log-Brunn-Minkowski inequality.
