I will discuss joint work with S. Starchenko, which combines dynamical systems in the nilmanifold setting with definable objects in o-minimal structures (e.g. semi-algebraic sets): Let G be a real algebraic unipotent group and let L be a lattice in G with p:G->G/L the quotient map. Given a subset X of G which is semi-algerbaic, or more generally definable in an o-minimal structure, we describe the closure of p(X) in terms of finitely many definable families of cosets of positive dimensional algebraic subgroups of G. The families are extracted from X, independently of L (using the model theoretic notion of "a complete type") .

We also note a dividing line among o-minimal structures between those in which the notions of equidistribution and topological density coincide and those where they might differ.

No prior knowledge in model theory is assumed.

We also note a dividing line among o-minimal structures between those in which the notions of equidistribution and topological density coincide and those where they might differ.

No prior knowledge in model theory is assumed.

## Date:

Thu, 02/05/2019 - 10:00 to 11:00