Symplectic fillings and star surgery

Laura Starkston
University of Texas, Austin
September 25, 2014
Although the existence of a symplectic filling is well-understood for many contact 3-manifolds, complete classifications of all symplectic fillings of a particular contact manifold are more rare. Relying on a recognition theorem of McDuff for closed symplectic manifolds, we can understand this classification for certain Seifert fibered spaces with their canonical contact structures. In fact, even without complete classification statements, the techniques used can suggest constructions of symplectic fillings with interesting topology.

Breaking \(e^n\) barrier for deterministic poly-time approximation of the permanent and settling Friedland's conjecture on the Monomer-Dimer Entropy

Leonid Gurvits
City University of New York
September 29, 2014
Two important breakthroughs on the permanent had been accomplished in 1998: A. Schrijver proved Schrijver-Valiant Conjecture on the minimal exponential growth of the number of perfect matchings in k-regular bipartite graphs with multiple edges; N. Linial, A. Samorodnitsky and A. Wigderson introduced a strongly poly-time deterministic algorithm to approximate the permanent of general non-negative matrices within the multiplicative factor en. Many things happened since them, notably the prize-winning Jerrum, Vigoda, Sinclair FPRAS for the permanent.