Arithmetic dynamics : Charles Favre (Ecole Polytechnique)

Summary: These lectures are aimed at presenting some aspects of the dynamics of polynomials in one variable with coefficients in a number field. We shall discuss two deep conjectures that have been proved to be very influential in the development of this field:  the uniform boundedness conjecture by Silverman, and the dynamical Andre-Oort conjecture Baker and DeMarco.  It will be the opportunity to present various tools coming from arithmetic geometry or from complex dynamics that are used to approach these challenging problems.

Level: M1                    

There will be preparatory lectures to cover some of the background material:

p-adic numbers: first 2-3 classes of the “Number Theory” seminar by Misha Finkelberg (Fridays 2pm, room 210, first class on September 14).

One-variable polynomials over complex numbers (Fatou and Julia sets), by Vladlen Timorin:

Monday           8.10 ----------- from 17:00 to 18:20, room 213

Thursday       11.10 ----------- from 17:00 to 18:20,  room 208

Lectures by C. Favre:  

Tuesday       16.10 ----------- from 17:00 to 18:20, room.208

Wednesday 17.10 -----------  from 17:00 to 18:20, room.208

Thursday      18.10 -----------  from 15:30 to 16:50, room.108

Monday         22.10 ----------- from 17:00 to 18:20, room.208

Tuesday        23.10 ----------- from 17:00 to 18:20, room.208

Wednesday  24.10 ----------- from 17:00 to 18:20, room.208

Thursday       25.10 ----------- from 17:00 to 18:20, room.208