## Departmental Colloquium

Sergei Starchenko

University of Notre Dame

The topological closure of algebraic and semi-algebraic flows on complex and real tori (joint work with Y.~Peterzil)

**Abstract:**Let $A$ be a complex abelian variety and $\pi\colon \mathbb{C}^n\to A$ be the covering map. It follows from a theorem of Ax that for an irreducible subvariety $X\subseteq \mathbb{C}^n$ the Zariski closure of $\pi(X)$ is a coset of an algebraic subgroup of $A$. In this talk we consider \emph{the topological closure} $\pi(X)$ of an algebraic subvariety $X$ of $\mathbb{C}^n$ and describe it in terms of finitely many algebraic families of cosets of real subtori. We also obtain a similar description when $A$ is a real torus and $X$ is a semi-algebraic set.

Friday October 27, 2017 at 3:00 PM in SEO 636