Workshop on Arithmetic and Complex Dynamics (17w5081)


(University of Cambridge)

Laura DeMarco (Harvard University)

Mattias Jonsson (University of Michigan)


The Casa Matemática Oaxaca (CMO) will host the "Workshop on Arithmetic and Complex Dynamics" workshop from November 12th to November 17th, 2017.

Complex dynamics is the study of repeated application of a self-map of a complex variety; a complex variety can be thought of as the solution set over the complex numbers of a system of polynomial equations in a (possibly large) number of variables. This study leads to mathematically interesting objects even for polynomial maps of the complex numbers, such as the Mandelbrot set. Arithmetic geometry concerns the study of solutions to systems of polynomials over a field where arithmetic makes sense; that is to say, where there is a notion of prime factorization in the field. In the past decade, deep connections have been found between the study of complex dynamics and arithmetic geometry, particularly through non-archimedean geometry. These connections have led to significant advances in traditional complex-dynamical questions, such as understanding degenerations of complex dynamical systems and the properties of positive entropy systems, as well as leading to new conjectures and discoveries in the arithmetic of dynamical objects. This workshop will focus on the interactions between complex and arithmetic methods in the study of dynamics in order to bring a diverse group of researchers up to date on recent developments and with a view toward potential progress and future applications.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry.

The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT.