To participate in this seminar, please register HERE.

To participate in this seminar, please register HERE.

A snowball is a self-similar surface that is obtained in a fashion analogous to the snowflake curve. The purpose of this talk is to show that these spaces may serve as deterministic toy models for the Brownian map. This is a random metric space that appears as the scaling limit of triangulations of the $2$-sphere. The self-similarity of a snowball may be represented by a rational map. Snowballs are quasispheres, i.e., quasisymmetrically equivalent to the standard $2$-sphere. This is closely related to the visual metric associated to the rational map being quasisymmetrically equivalent to the spherical metric on the Riemann sphere.

To participate in this seminar, please register HERE.

Just as Per_1 houses the illustrious Mandelbrot set, so too does Per_n a combinatorial fractal object. In yet another talk about everybody's favorite variety, we’ll see how polynomials with super-attracting n-cycles naturally give rise to rational dynamics, by ways such as matings and captures. With these concepts we will discuss in detail the combinatorics for n<=5 and indicate a strategy to prove Per_n is connected. 

To participate in this seminar, please register HERE.

Join us for math discussions with Professor Hubbard. All are welcome! Younger researchers in particular are encouraged to attend. If you have questions about the semigroup, please email Sarah at kochsc@umich.edu

To participate in this seminar, please register HERE.

The Julia set of many exponential maps consists of an uncountable collection of pairwise disjoint curves that tend to infinity. In 1999, Karpińska proved the following surprising result: the set of endpoints of these curves has Hausdorff dimension 2, while the set of curves without endpoints has Hausdorff dimension 1. In this talk, we will comment on the main ideas of the proof, implications and generalizations.

This seminar is for postdocs and PhD students, and we kindly ask faculty not to attend.

To participate in this seminar, please register HERE.

In this talk I will describe Sharkovskii's classical result for periodic points of a continuous self-map of an interval. I will then introduce some basic concepts in complex dynamics. I will describe the Mandelbrot set as well as a combinatorial structure of the hyperbolic components. Finally I will describe how Sharkovskii's ordering, as well as generalized versions of it, are found on the Mandelbrot set.

This seminar is for postdocs and PhD students, and we kindly ask faculty not to attend.

To participate in this seminar, please register HERE.

To participate in this seminar, please register HERE.

The conformal field theory of Kang and Makarov is a mathematician's take on how the physicists think about CFT and the Coulomb gas. I will try to explain the many aspects of the Kang-Makarov approach, focusing on the geometrical characterizations, the underlying potential theory, and the connection with martingale observables for SLE type processes.

To participate in this seminar, please register HERE.

Join us for an informal group discussion of some of the exciting math that happened over the past semester at MSRI. We will talk about progress that was made, open problems, possible future directions, etc.