שלחו לחבר

Smooth parametrizations (of semi-algebraic, o-minimal, … sets), and their applications in Dynamics, Analysis, and Diophantine geometry (and, maybe, in Complex Hyperbolic Geometry)

Seminar
Speaker
Prof. Yosef Yomdin, Weizmann Institute
Date
16/04/2018 - 15:15 - 14:00
Place
2nd floor Colloquium Room, Building 216
Abstract

Smooth parametrization consists in a subdivision of a mathematical object under consideration into simple pieces,
and then parametric representation of each piece, while keeping control of high order derivatives. Main examples
for this talk are C^k or analytic parametrizations of semi-algebraic and o-minimal sets.
We provide an overview of some results, open and recently solved problems on smooth parametrizations, and their
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 plan to stress.
We consider a special case of smooth parametrization: ``doubling coverings” (or “conformal invariant Whitney coverings”),
and “Doubling chains”. We present some new results on the complexity bounds for doubling coverings, doubling chains,
and on the resulting bounds in Kobayashi metric and Doubling inequalities. We plan also to present a short report on
a remarkable progress, recently achieved in this (large) direction by two independent groups (G. Binyamini, D. Novikov,
on one side, and R. Cluckers, J. Pila, A. Wilkie, on the other).

תאריך עדכון אחרון : 11/04/2018