My favorite talk on the first day came from the best student paper winner, Ryan Williams on Better Time-Space Lower Bounds for SAT and Related Problems though I'm a bit biased since he's improving on some of my earlier work. He shows SAT cannot be solved by a random-access machine using nc time and no(1) space for c slightly larger than the square root of 3 (about 1.732) improving on the previous lower bound of 1.618. He had several clever ideas recursing on the previous techniques. One can hope that by extending these techniques to push the lower bound to any c<2. Above 2 you seem to lose any advantage from doing recursion.
Today Manuel Blum given an invited talk taking "steps towards a mathematical theory of consciousness." More on that and the rest of the conference later.