Computer Science/Discrete Mathematics Seminar II

I will discuss the difficult problem of proving reasonable bounds in the multidimensional generalization of Szemerédi's theorem. Most of the first talk will be spent going over Shkredov's proof of good bounds for sets lacking corners, in preparation for the second talk, where I'll describe a proof of reasonable bounds for sets lacking nontrivial configurations of the form $(x,y), (x,y+z), (x,y+2z), (x+z,y)$ in the finite field model setting.