Seminario de Álgebra

Viernes 7 de julio a las 11:30 en el aula 520 del módulo 17

Conferenciante: Ya'acov Peterzil (Univesity of Haifa)

Título: The topological closure of algebraic and o-minimal flows in compact tori

Abstract: Let p:C^n ->A be the covering map of a complex abelian variety and let X be an algebraic sub-variety of C^n, or more generally a definable set in an o-minimal expansion of the real field. Ullmo and Yafaev investigated the topological closure of p(X) in A in the above two settings and conjectured that the frontier of p(X) can be described, when X is algebraic, as finitely many cosets of real subtori of A.  They proved the conjecture when dim X=1.
In recent work we prove a modified version of the conjecture (it fails as stated) , giving a complete description of the topological closure of p(X), for an algebraic X. in an arbitrary compact complex torus. We prove a similar result when p:R^n->T is the covering map of a compact real torus and X a subset of R^n which  is definable in an o-minimal structure.
The result uses methods from model theory as well as some basic theory of lattices in R^n.
(Joint work with Sergei Starchenko)