UWashington-PIMS Mathematics Colloquium: Bryna Kra

Since Szemeredi's Theorem and Furstenberg's proof thereof using ergodic theory, dynamical methods have been used to show the existence of numerous patterns in sets of positive upper density. These tools have led to uncovering new patterns that occur in any sufficiently large set of integers, but until recently all such patterns have been finite. Resolving questions and conjectures of Erdos, we use dynamical methods to prove a density version of the finite sums theorem of Hindman. This is joint work with Joel Moreira, Florian Richter, and Donald Robertson.