Computer Science/Discrete Mathematics

The degree mantra states that any non-zero univariate polynomial of degree at most d has at most d roots (counted with multiplicity). A generalization of this to the multivariate setting, proved by Dvir-Kopparty-Saraf-Sudan asserts that over any...

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...

This talk will serve as an introduction to the random algebraic method. This method has its origins in the following problem: suppose the binomial random graph comes "close" to having some property of interest P, but fails to do so because of the...