To answer one of Lance's previous posts, the Internet is definitely harming conferences: most everyone who stayed up until 5 AM to watch the Red Sox beat the Yankees in 14 innings on MLB.TV has not made it to James Lee's talk at 8:30 AM on embeddings (in fact I think I'm the only one who did make it here). Krauthgamer, Lee, Mendel, and Naor presented a powerful new method for constructing embeddings of finite metric spaces called measured descent which, among other things, implies optimal volume-respecting embeddings (in the sense of Feige).
I checked the registration numbers and indeed only 172 people have officially registered for the conference—that's 100 less than the registration at STOC in Chicago.
Yesterday I mentioned the winners of the best paper award. I should also mention the best student paper award winners: Lap Chi Lau's An Approximate Max-Steiner-Tree-Packing Min-Steiner-Cut Theorem shared the prize with Marcin Mucha and Piotr Sankowski's Maximum Matchings via Gaussian Elimination. Lau's paper gives the first constant factor approximation to the problem of finding a large collection of edge-disjoint trees that connect an undirected multigraph. Mucha and Sankowski give a nice method for finding maximum matchings in general graphs in time O(nω) where ω is the matrix multiplication exponent. Lovász showed how to test for a matching in a graph using matrix multiplication, and Mucha and Sankowski extend this and actually recover the matching.
Valiant's talk on Holographic Algorithms was well attended: he described a new, quantum-inspired method for constructing polynomial-time algorithms for certain counting problems. The algorithms are classical (no quantum required) and give the first efficient solutions for problems such as PL-Node-Bipartition: find the cardinality of a smallest subset of vertices V' of a max-degree 3, planar graph such that deletion of V' (and its incident edges) causes the graph to become bipartite. At the end he gave a simple criterion for proving P = P#P via these techniques!