Much of the early development of model theoretic stability theory was motivated by stable groups, which include algebraic groups as guiding examples. Later work of Hrushovski and Pillay showed that many tools from stable group theory can be adapted to the local setting, where one works around a single stable formula rather than a stable theory. More recently, groups definable in NIP theories have been intensively studied, bringing back the importance of measures in model theory. On the other hand, local NIP group theory is not as well understood. This talk will start by surveying some of these results. I will then present recent work (joint with Pillay) on NIP formulas in pseudofinite groups, which leads to a potential localization of the notion of NIP groups with finitely satisfiable generics. This research was motivated by questions from additive combinatorics concerning tame arithmetic regularity lemmas, and this talk will provide some of the model theoretic background of my talk the following day on these combinatorial applications.
Wed, 06/06/2018 - 11:00 to 13:00