THEMATIC PROGRAMS

November 27, 2014

Mailing List : To receive updates on the program please subscribe to our mailing list at www.fields.utoronto.ca/maillist

October 27-28, 2008
Mini-workshop on p-adic dynamics

Organizer: Joseph Silverman
Speakers: Rob Benedetto, Robert Rumely and Joseph Silverman

Mini - workshop Schedule

Monday October 27
9:30-10:15 am Tutorial on p-adic numbers, Q_p and C_p, and p-adic analysis
A lecture designed for people who are unfamiliar with p-adic numbers and p-adic fields. The talk will cover p-adic (nonarchimedean) absolute values, the field of p-adic rationals Q_p and its algebraic extensions, and the algebraically closed and complete (but not spherically complete) p-adic field C_p.
10:15-11:00 Coffee Break
11:00-12:00 Introduction to p-adic dynamics
Rob Benedetto
As the title indicates, this talk will be an introduction to p-adic dynamics, including a discussion of periodic points, (attracting, repelling, indifferent), the p-adic Fatou and Julia sets, disk-components and analytic components, wandering domains, and other topics as time permits. The talk will include numerous examples.
12:00- 1:30 pm Lunch Break
1:30-2:30 Berkovich space and dynamics on Berkovich space
Bob Rumely
This talk will begin with a description of the Berkovich projective line over a complete, algebraically closed nonarchimedean field, and the way that a rational function acts on the Berkovich projective line. It will then compare the dynamics of a rational function on the classical projective line over the complex numbers and on the Berkovich projective line, focusing on the theory of periodic points and Fatou-Julia theory.
2:30- 3:00 Coffee Break
3:00-4:00 A survey of (global) arithmetic dynamics
Joe Silverman
Arithmetic dynamics is the study of dynamical systems from a viewpoint derived from the classical theory of Diophantine equations and arithmetic geometry. I will explain this correspondence and describe some of the main results and conjectures in the area, in particular those related to rationality of periodic points and integrality of wandering points. Additional topics, as time permits, will include dynamical canonical heights, dynamical analogues of theorems of Faltings and Raynaud, reduction modulo p, and dynamical analogues of cyclotomic fields and cyclotomic units.
Tuesday October 28
11:00-12:00 Applications of p-adic dynamics
Rob Benedetto
This talk will focus on applications of p-adic dynamics, including strong (non-uniform) bounds for global periodic points.
12:00- 1:30 pm Lunch Break
1:30-2:30 Nonarchimedean potential theory and dynamical applications
Bob Rumely
This talk will describe the Laplacian on the Berkovich projective line and will use it to construct the "canonical measure" associated to a rational function of degree at least 2, which is analogous to the classical invariant measure constructed by Brolin, Lyubich, and Freire-Lopes-Man\'e. It will then discuss equidistribution theorems relative to this measure, and use them to derive structural information about the Berkovich Julia set.
2:30- 3:00 Coffee Break
3:00- 4:00
Families of dynamical systems and their associated moduli spaces
Joe Silverman
In the first part of this talk I will discuss the construction of parameter and moduli spaces associated to families of rational functions, including the use of mulitplier systems, an explicit description of the moduli space of rational maps of degree two, and a sampling of open questions concerning such spaces. The second part will focus on the dynamical modular curves that classify quadratic polynomials having a specified periodic point structure, analogous to classical elliptic modular curves. The third part will describe relations between the field of definition and the field of moduli of a rational map.

 

November 10 - 14, 2008
Mini-workshop on complex dynamics

Organizers: Jeff Diller, Eric Bedford
Speakers: Nessim Sibony, Mattias Jonsson, Henri De Thelin, Jeff Diller, Eric Bedford

Mini- workshop Schedule
(speaker abstracts)

Monday November 10, 3rd Floor Stewart Library
9:00- 10:00 am Holomorphic maps and entropy: Background and guiding principles
Jeffrey Diller
10:00- 10:15 Break
10:15- 11:15 Equidistribution problems in holomorphic dynamics
Nessim Sibony
11:15- 11:30 Break
11:30- 12:30 Dynamics of polynomial diffeomorphisms
Eric Bedford
Tuesday November 11, Room 230
9:00- 10:00 am Rational surface maps: geometric issues
Jeffrey Diller
10:00- 10:15 Break
10:15- 11:15 Equidistribution (cont'd)
Nessim Sibony
11:15- 11:30 Break
11:30- 12:30 Dynamics of polynomial diffeomorphisms (cont'd)
Eric Bedford
Wednesday November 12, Room 230
9:00- 10:00 am Rational surface maps: analytic issues
Jeffrey Diller
10:00- 10:15 Break
10:15- 11:15 Dynamics of meromorphic maps on compact Kahler manifolds
Henri De Thelin
11:15- 11:30 Break
11:30- 12:30 Surface dynamics and the Riemann-Zariski space
Mattias Jonsson
Thursday November 13, Room 230
9:00- 10:00 am Superattracting fixed points
Mattias Jonsson
10:00- 10:15 Break
10:15- 11:15 Equidistribution (cont'd)
Nessim Sibony
11:15- 11:30 Break
11:30- 12:30

Dynamics of meromorphic maps (cont'd)
Henri De Thelin

Friday November 14, Room 230
9:30- 10:30 Polynomial dynamics at infinity
Mattias Jonsson
10:30- 11:00 Break
11:00- 12:00 Dynamics of meromorphic maps (cont'd)
Henri De Thelin

For additional information contact thematic(PUT_AT_SIGN_HERE)fields.utoronto.ca

Back to Top