Date/Time Date(s) - 03/03/20231:30 pm - 2:30 pm
Speaker: Amador Martín-Pizarro, University of Freiburg Title: Corners and stability
Abstract: Given an abelian group G, a corner is a a subset of pairs of the form (x,y),(x+g,y),(x,y+g) with g non trivial. Ajtai and Szemerédi proved that, asymptotically for finite abelian groups, every dense subset S of G×G contains a corner. Shkredov gave a quantitative lower bound on the density of the subset S. In this talk, we will explain how model-theoretic conditions on the subset S, such as local stability, will imply the existence of corners and of other configurations for (pseudo-)finite abelian groups. This is joint work with D. Palacin (Madrid) and J. Wolf (Cambridge).
Location: Hamilton Hall, Room 312