Department of Mathematics

Conference Schedule

Registration and Breaks: Mathematics Library on the 3rd Floor of the Mathematical Sciences Building (MATH).

Lectures: Recitation Building Room 112 (REC 112) .

Saturday, October 10, 2009

Sunday, October 11, 2009

Abstracts

Tobias Ekholm (Uppsala)

Title: Legendrian surgery, contact-, and symplectic homology

Abstract: We describe how Legendrian surgery affects contact and symplectic homology. The description leads in particular to a combinatorial description of the symplectic homology of any 4-dimensional Liouville domain.

Viktor Ginzburg (UCSC)

Title: The action-index spectrum and periodic orbits of Hamiltonian systems

Abstract: The main theme of this talk is a connection between the existence of infinitely many periodic orbits for a Hamiltonian system and the behavior of its action or index spectrum under iterations. The idea can, perhaps, be illustrated by the "classical" Ljusternik-Schnirelman theory where, on the one hand, simple topological considerations lead to a lower bound on the number of critical values of a function and, on the other hand, this lower bound translates in an obvious way into a lower bound for the number of critical points. Likewise, one can use the action-index spectrum, accessible via Floer theory, as a tool detecting, under favorable circumstances, whether or not a Hamiltonian diffeomorphism has infinitely many periodic points. In this talk, based on a joint work with Basak Gurel, we will discuss and prove some specific results of this type.

Tara Holm (Cornell)

Title: Symplectic reduction in stages and orbifold invariants

Abstract: Let M be a compact symplectic manifold endowed with a Hamiltonian torus action. I will discuss how to extend the well-known result that components of a moment map for the action are Morse-Bott functions on M to make arguments about the topology of a partial level set. This may be used to make conclusions about orbifold invariants of symplectic quotients. The talk will include many examples, including toric orbifolds and quotients of coadjoint orbits by subtori of the maximal torus.

Mark McLean (MIT)

Title: Computability and exotic contact manifolds

For each n>6, we construct (mainly using handle attaching) a list of contact manifolds C1,C2,C3,... diffeomorphic to the sphere of dimension 2n-1 such that there is no algorithm that tells you which of these manifolds are contactomorphic to C1. The idea of the proof is to reduce this problem to the word problem for groups.

Leonid Polterovich (Chicago)

Title: Lie quasi-states

A real-valued function on a Lie algebra is called a quasi- state if it is linear on all abelian subalgebras. We address the question of uniqueness of quasi-states on the symplectic Lie algebra. We discuss links to foundations of quantum mechanics (the Gleason theorem) as well as to the group-theoretic notion of a quasi-morphism. Joint work with Michael Entov.