Quite a few remarkable talks recently that I thought I'd write briefly about, especially the last one.
Jim Peebles gave a lecture last week about "finding" the big bang (cosmic microwave background and that kind of thing). An interesting account of the historical developments. As physics improves by successive approximations, it always leaves something unknown for the next generation to find out.
Rodney Baxter gave a talk on his work on hard hexagons, and had lessons about publishing conjectures even if you don't fully understand them, so others can work on them too.
Slava Rychkov gave a talk about ideas that might be pretty exciting for future work. Essentially, they use conformal field theory techniques ("conformal bootstrap") with some success in greater than two space dimensions (e.g. on the 3D Ising model), complementing the use of renormalisation group techniques.