Measures in NIP theories and applications to combinatorics – Pierre Simon (CNRS, Université Lyon)

Venue

Sala Riunioni (Dip. Matematica).

Abstract

The study of NIP theories has brought forth a new tool in model theory : Keisler measures, or finitely additive measures on definable sets. In this talk, I will introduce both NIP and Keisler measures and survey the most notable results concerning them. I will state the theorem of Vapnik and Chervonenkis giving a uniform law of large numbers for families of finite VC-dimension, give some model-theoretic consequences. Discuss generically stable and smooth measures and give applications to regularity lemmas in finite combinatorics.

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