
THEMATIC PROGRAMS 

September 17, 2014  
THEMATIC
PROGRAM ON ARITHMETIC GEOMETRY, HYPERBOLIC GEOMETRY AND RELATED
TOPICS

October 27  28, 2008

November 10  14, 2008

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October 2728, 2008
Miniworkshop on padic dynamics
Organizer: Joseph Silverman
Speakers: Rob Benedetto, Robert Rumely and Joseph Silverman
Monday October 27  
9:3010:15 am  Tutorial on padic numbers, Q_p and C_p,
and padic analysis A lecture designed for people who are unfamiliar with padic numbers and padic fields. The talk will cover padic (nonarchimedean) absolute values, the field of padic rationals Q_p and its algebraic extensions, and the algebraically closed and complete (but not spherically complete) padic field C_p. 
10:1511:00  Coffee Break 
11:0012:00  Introduction to padic dynamics Rob Benedetto As the title indicates, this talk will be an introduction to padic dynamics, including a discussion of periodic points, (attracting, repelling, indifferent), the padic Fatou and Julia sets, diskcomponents and analytic components, wandering domains, and other topics as time permits. The talk will include numerous examples. 
12:00 1:30 pm  Lunch Break 
1:302:30  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 FatouJulia theory. 
2:30 3:00  Coffee Break 
3:004:00  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  
11:0012:00  Applications of padic dynamics Rob Benedetto This talk will focus on applications of padic dynamics, including strong (nonuniform) bounds for global periodic points. 
12:00 1:30 pm  Lunch Break 
1:302:30  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 FreireLopesMan\'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
Miniworkshop on complex dynamics
Organizers: Jeff Diller, Eric Bedford
Speakers: Nessim Sibony, Mattias Jonsson, Henri De Thelin, Jeff
Diller, Eric Bedford
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 RiemannZariski 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) 
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@fields.utoronto.ca