Speaker: Joel Moreira (Warwick)
Title: Finding infinite patterns in sets with positive density
Abstract: Old questions in additive combinatorics and Ramsey theory ask what infinite patterns are unavoidable in sets of natural numbers with positive density, but until recently, there were no positive answers. In the last few years a new technique was developed to address such questions, making use of ergodic theory and dynamical systems, which were previously restricted to handling finite patterns.
In this talk I will briefly survey the history of the subject, explain the connection to ergodic theory, and describe how we used this technique to answer a question of Paul Erdos regarding infinite sumsets. The talk will be based on joint work with Bryna Kra, Florian Richter and Donald Robertson.