Pierre Simon

Mathematics Department, University of California, Berkeley (United States)


Model Theory

Measures, groups and the NIP condition

The study of definable groups plays an important role in model theory, both pure and applied. Of particular importance are notions of genericity, or largeness, for definable subsets of groups. In the last decade, groups with translation-invariant measures have attracted much attention. Their study involves tools from pure model theory, measure theory and topological dynamics. Such groups are especially well behaved under the so-called NIP condition.

This tutorial will be an introduction to definable groups with invariant measures. So as to avoid going to deep into technicalities, I will present a series of small topics and in particular emphasize the variety of tools involved.

Here is a tentative outline of the tutorial:

  • Introduction to definable groups.
  • Amenable groups and Haar measures on compact groups. • Definably amenable groups; compact quotients; examples. • The NIP condition and consequences.
  • Interesting subclasses and applications.


Pierre Simon works in model theory. His research so far has focused on NIP theories, a class which generalizes both stable and o-minimal theories. This topic has links with combinatorics, rigid geometry and topological dynamics, areas where the NIP condition appears in various guises.

Simon obtained his PhD from Université d'Orsay in 2011, after which he was a postdoc at the Hebrew University, Jerusalem. He then held a CNRS position in Lyon before becoming assistant professor at Berkeley in 2016.

He was awarded the Sacks prize and the Perrissin-Pirasset/Schneider prize from the Chancellerie des Universités de Paris for his dissertation.