# Seminars

## TODAY

Spherical metrics with conical singularities: existence, non-existence, and moduli

**Speacker:**

*Dmitri Panov*- King's College London

**Differential Geometry**

**Abstract: **I'll speak about my joint work with Gabirele Mondello. We are interested in the following questions.1) For which n-tuples of angles there exists a genus g surface with metric of curvature 1 and conical singularities of these given angles?2) Can the moduli space of metrics with fixed angles be disconnected?3) Does existence of the metric impose restrictions on the conformal class of the pointed surface?

I will report on our solution to all these questions.

## UPCOMING

Foliations with a transversely homogeneous component in the singular set

**Speacker:**

*Alcides Lins Neto*- IMPA

**Holomorphic Foliations**

**Abstract: **In this talk we intend to prove that a codimension one foliation on $\mathbb{P}^n$, $n\ge3$, that is a local product near every point of some codimension two irreducible component of the singular set has a rational first integral. This result is a kind of generalization of a result of Calvo Andrade and M. Brunella about foliations with a Kupka component.

ICM2018 Experience

**Speacker:**

*Roberto Beauclair*- IMPA

**Special Talk**

**Abstract: **Será relatada a participação do grupo de TI do IMPA no desenvolvimento de softwares e implantação de servidores como suporte às atividades do ICM2018.Serão mostrados e detalhados todos os programadas desenvolvidos, bem como a infraestrutura básica de banco de dados, servidores Web, aplicativo *mobile* e soluções para as TVs de notícias do evento.

Satellite copies of the Mandelbrot set

**Speacker:**

*Luna Lomonaco*- USP

**Ergodic Theory**

**Abstract: **For a polynomial on the Riemann sphere, infinity is a (super) attracting fixed point, and the filled Julia set is the set of points with bounded orbit. Consider the quadratic family $P_c(z)=z^2+c$. The Mandelbrot set M is the set of parameters c such that the filled Julia set of $P_c$ is connected. Douady and Hubbard proved the existence of homeomorphic copies of M inside of M, which can be primitive (roughly speaking the ones with a cusp) or a satellite (without a cusp). Lyubich proved that the primitive copies of M are quasiconformally homeomorphic to M, and that the satellite ones are quasiconformally homeomorphic to M outside any small neighbourhood of the root. The satellite copies are not quasiconformally homeomorphic to M, but are they mutually quasiconformally homeomorphic? In a joint work with C. Petersen we prove that this question has in general a negative answer.