Analysis and Dynamics (16w5129)

Arriving in Oaxaca, Mexico Sunday, September 18 and departing Friday September 23, 2016

Organizers

(Institute of Mathematics of Polish Academy of Sciences)

Jacek Graczyk (Université Paris-Sud)

Neil Dobbs (University of Geneva)

Objectives

The main purpose of the workshop is to bring researchers together, who may not otherwise meet, to discuss the recent developments of dynamical systems in one complex variable and in one real variable from the analyst’s point of view. Through a relaxed and stimulating environment, we hope to inspire new questions, ideas and collaborative projects. The interplay between dynamics and analysis will be highlighted as we renew and rejuvenate the links between these domains.

We shall bring together a mid-sized, high quality group of younger and more experienced participants from diverse countries and from the various strands of mathematics related to the theme of the workshop. In the workshop spirit, we shall focus on presenting ideas and tools that may lead to further progress and collaboration.

The directions for future research will guide the focus of the workshop.

1) Transfer tools and methods from several complex variables to further study dynamics in one complex variable. Individual dynamical systems, their ergodic theory and geometric structure are of interest, as are questions regarding structure and properties of parameter space and the relation between local structure of parameter space and the corresponding dynamics.

2) Explore the links between random fractals, analysis on fractals, and dynamical systems. To each parameter in one-dimensional dynamics corresponds a natural, irregular fractal. Harmonic or other probability measures living in parameter space therefore define random fractals (the corresponding Julia sets). These fractals can be very irregular (even stretching the definition of the term fractal), and analysis on such sets is ripe for further development.

3) Cast a new light on complex analysis from the dynamical systems perspective. We hope participants will raise new questions and new ways of looking at long-standing problems in analysis, whether related to quasiconformal analysis, quasisymmetric maps, geometry of curves, or big conjectures such as Brennan's or the Carleson-Jones conjecture.

Along with (the listed) core of experienced researchers, we plan to invite a balanced number of graduate students and post-doctoral researchers who will benefit from exposure to multifaceted mathematical approaches to their subjects of interest. We hope this will also promote a long-term rapprochement between researchers in dynamics and analysis.