Sophie Stevens

Sums, Products, Additive Combinatorics, Etc.

For a set of numbers A, we can make its sum set A+A by considering all pairwise sums, and its product set AA from all pairwise products. A fundamental principle of additive combinatorics is that it is impossible for both the sum set and the product set to be simultaneously large (as compared to the cardinality of A). I will talk about recent progress on this problem in finite fields, and, time permitting, related work in the reals concerning convex sets.
These results are joint work with Ali Mohammadi and Audie Warren.