Colloquium: Tuesday, March 21, 2 pm. Speaker: Kobi Peterzil (Haifa). Title: “Algebraic and definable flows on complex and real tori”.
Consider a compact complex torus T, identified with the quotient C^n/L, where L is a lattice in C^n. Let p: C^n->T be the quotient map. Ullmo and Yafaev have recently asked the following question:
Assume that X is an algebraic subvariety of C^n, what is the topological closure of p(X) in T?
When dim X=1 they showed that the frontier of p(X) consists of finitely many cosets of REAL sub tori of T and conjectured the same result for arbitrary dimension.
In joint work with S. Starchenko, we answer their question by a modified version of the original conjecture, and describe the frontier of p(X) as a finite union of (possibly infinite) families of cosets of fixed real sub tori of T. We give a similar answer to another question of theirs when p:R^n->T is the projection onto a real torus and X is a subset of R^n definable in an o-minimal structure.
Both results naturally go via a model theoretic analysis of types on X and make use of results about model theory of valued fields and o-minimal structures. All notions will be explained.
