I'm spending (part of) the week at "The Power of Randomness in Computation Workshop", an IMA (Institute for Mathematics and its Applications) and ARC (Georgia Tech Algorithm and Randomness Center) co-sponsored workshop at Georgia Tech. Here's the schedule. I'm told slides will eventually be put up somewhere on the IMA website for such things. Great organization at Georgia Tech -- a big crowd in a very nice room, lots of food and coffee, all very well organized. They even had Ben Affleck waiting in front of the building for us this morning. He seemed to be a little busy shooting a movie to greet us properly, but maybe he'll have a bit more time to chat tomorrow.
Besides Ben, a few other highlights:
Leslie Goldberg started things of talking about the complexity of approximating complex-valued Ising and Tutte partition functions. I remember the Ising/Tutte models (mostly from graduate school and shortly after); now there are connections between various problems in quantum computing and these functions on complex values, which (or course) I had not known.
Nike Sun gave a talk on the exact k-SAT threshold (for large k). It was very clearly presented and gave the argument at the intuitive level. I gained some insight into why the "locally random tree" type
argument I've enjoyed in coding/belief propagation arguments breaks down
in certain satisfiability problems, due to clustering of solutions and
other challenging correlations, and how those issues can be handled. I started to understand (I think) the point of replica symmetry breaking arguments and how they were used to guide the analysis of the k-SAT problem.
Other talks from the day: Amin-Coja Oghlan also talked about replica symmetry techniques and their uses for random graph coloring problems, Eli Upfal talked about some new shuffling techniques for oblivious storage dubbed the Melbourne shuffle, Aravind Srinivasan gave a talk on the Lovasz Local Lemma (staring from the Moser-Tardos results and showing how these arguments carry forward and give greater power and insight into the use of the LLL for additional problems), and I talked about invertible Bloom lookup tables and briefly mentioned a few other unrelated things in progress.