SEMINARS
Updated: 12-16-2009

   

DECEMBER 2009
   
Department Colloquium
Topic: Ideas around Symplectic Field Theory
Presenter: Helmut Hofer, IAS
Date:  Wednesday, December 16, 2009, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: Symplectic Field Theory (SFT) is the study of (pseudo-)holomorphic curves in symplectic cobordisms and contains Gromov-Witten theory and symplectic Floer theory as special cases. The algebraic invariants of SFT are obtained by a simultaneous study of infinitely many interdependent first order elliptic systems which exhibit compactness and transversality issues. A treatment of SFT with classical (nonlinear) Fredholm theory, though possible, would be extremely cumbersome. This lead to the development of a new generalized Fredholm theory in a new class of general spaces called polyfolds. In the talk a certain number of ideas are described which might be also useful in different contexts.
   
Discrete Mathematics Seminar
Topic: The k edge-disjoint paths problem in digraphs with bounded independence number
Presenter: Alexandra Ovetsky Fradkin, Princeton University
Date:  Thursday, December 17, 2009, Time: 2:15 p.m., Location: Fine Hall 224
Abstract:

In 1980, Fortune, Hopcroft, and Wyllie showed that the following algorithmic problem (k-EDP) is NP-complete with $k=2$: k Edge-Disjoint Paths (k-EDP) Instance: A digraph $G$, and $k$ pairs $(s_1,t_1),...,(s_k,t_k)$ of vertices of $G$.

Question: Do there exist directed paths $P_1,...,P_k$ of $G$, mutually edge-disjoint, such that $P_i$ is from $s_i$ to $t_i$ for $i=1,...,k$?

In this talk we will present a polynomial time algorithm to solve $k$-EDP for fixed $k$ in digraphs with independence number at most $2$. We will also talk about progress made towards solving $k$-EDP in digraphs with independence number at most $\alpha$, for fixed $\alpha$. This is joint work with Paul Seymour.

   
Topology Seminar
Topic: Bordered Floer homology and factoring mapping classes
Presenter: Peter Ozsvath, Columbia University
Date:  Thursday, December 17, 2009, Time: 4:30 p.m., Location: Fine Hall 314
Abstract: I will discuss "bordered Floer homology", an invariant for three-manifolds with parameterized boundary. The theory associates a differential graded algebra to a (parameterized) surface; and a module over that algebra to a three-manifold which bounded by the surface. I will describe this construction, and then focus on computational aspects of this theory, including an algorithm for calculating HF-hat of closed three-manifolds, obtained by factoring mapping classes. This is joint work with Robert Lipshitz and Dylan Thurston.