Colloquium: Tuesday, January 10, 2 pm. Speaker: Yosef Yomdin (Weizmann). Title: “Smooth parametrizations, and their applications in dynamics, analysis, and Diophantine geometry”.
Smooth parametrization consists in a subdivision of a mathematical object under consideration into simple pieces, and a parametric representation of each piece, while keeping control of high order derivatives. The main goal of this talk is to provide an overview of some results and open problems on smooth parametrization and its applications in several apparently rather separated domains: Smooth Dynamics, Diophantine Geometry, and Analysis. The structure of the results, open problems, and conjectures in each of these domains shows in many cases a remarkable similarity, which we’ll stress.
We consider a special case of smooth parametrization: “doubling coverings” (or “conformal invariant Whitney coverings”). We present some new results on the complexity bounds for doubling coverings, and on the resulting bounds in “Doubling inequalities”.
