For those of you in Toronto, you might want to stop by at UofT next Friday for a talk on P vs. NP. Here is the description:
Title: Can the P vs NP question be independent of the axioms of mathematical reasoning?
Speaker: Shai Ben-David, University of Waterloo
Venue: Galbraith Bld, Rm. 248
Time: 18 November, 11.10 AM
I'll discuss the possibility that the failure to resolve basic complexity theoretic statements stems from these statements being independent of the logical theories that underly our mathematical reasoning. In the first part of the talk, I shall briefly survey independence (from the axioms of set theory) of questions in various areas of mathematics. I shall then go on to discuss independence results that seem relevant to the P vs NP question. Finally, I shall outline some results of myself and Shai Halevi that imply that, as far as current proof techniques for such questions go, the task of proving that P vs NP is independent of Peano Arithmetic is as hard as proving very strong upper bounds on the (deterministic) complexity of the SAT problem.