Schedule

Virtual mingle

An earlier start in case you want to say hi to colleagues and friends

Welcoming words

José Seade

Conformal dynamics: Julia sets, Kleinian groups, and Schwarz reflections

Misha Lyubich

We will discuss the interplay between three branches of Conformal Dynamics: iteration of (anti-)rational maps, actions of Kleinian groups, and dynamics generated by Schwarz reflections in quadrature domains. We will show examples of Schwarz reflections obtained by matings between anti-quadratic maps and the triangle modular group, and examples of Julia reasizations for Apollonian-like gaskets. Some of these examples can be turned into others by means of a David surgery.

Amenability in rational maps

Carlos Cabrera

We discuss some intersection properties of holomorphic dynamical systems which derive into algebraic, dynamical and ergodic relations such as the amenability of associated semigroups and measures of maximal entropy. This is a joint work with Peter Makienko.

On torsion of discrete isometry groups of negatively curves manifolds

Misha Kapovich

It is a classical theorem of Selberg that every finitely generated isometry group of a symmetric space (i.e. a finitely generated group of matrices with real coefficients) contains a finite index torsion-free subgroup. In his 1974 ICM talk Margulis asked if the same property holds for isometry groups of Hadamard manifolds (complete, simply connected manifolds of nonpositive curvature). In the talk I will prove that Selberg's property fails already for discrete isometry groups of negatively curved Hadamard manifolds of dimension 4. I will also explain why Selberg's property holds for 3-dimensional Hadamard manifolds.

Closing words

Peter Makienko

A concert by Ekaterina Belyaeva

Facebook Live: https://www.facebook.com/svetlana.tkachenko.754

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