Appears in collection : 2018 - T1 - WS1 - Model theory and combinatorics

We use local stability theory to prove a group version of Szemer´edi regularity for stable subsets of finite groups. Toward generalizing this result to the NIP setting, we consider definable set systems of finite VC-dimension in pseudofinite groups. In this case, many tools and results from groups definable in NIP theories can be localized, and we study group-theoretic versions of Szemer´edi regularity which can be shown using these methods. Joint with A. Pillay and C. Terry.