So I can only give my very brief thoughts on the talks. For more information, go here.

Atri Rudra was up first with a neat way to generalize joins, inference in probabilistic models and even matrix multiplication all within a generic semi-ring framework, which allowed the authors to provide faster algorithms for join estimation and inference. In fact, these are being used right now to get SOTA join implementations that beat what Oracle et al have to offer. Neat!

Vasilis Syrgkakis asked a very natural question: when players are playing a game and learning, what happens if we treat

*all*players as learning agents, rather than analyzing each player's behavior with respect to an adversary? It turns out that you can show better bounds on convergence to equilibrium as well as approximations to optimal welfare (i.e the price of anarchy). There's more work to do here with more general learning frameworks (beyond bandits, for example).

Chris Umans talked about how the resolution of the cap set conjecture implies bad news for all current attempts to prove that $\omega = 2$ for matrix multiplication. He also provided the "book proof" for the cap set conjecture that came out of the recent flurry of work by Croot, Lev, Pach, Ellenberg, Gijswijt and Tao (and cited Tao's blog post as well as the papers, which I thought was neat).

I hope the slides will be up soon. If not for anything else, for Atri's explanation of graphical models in terms of "why is my child crying", which so many of us can relate to.