# Algebraic Geometry and Hyperbolic Geometry – New Connections

Hotel La Plage, Cabo Frio, Rio de Janeiro, de 17/06 até 21/06

## Aim and Scope

The main purpose of the conference is to bring together researchers in algebraic and hyperbolic geometry, to foster further mutually beneficial interaction between the two fields.

The uniformization theorem for Riemann surfaces is the traditional and best known bridge between algebraic geometry and hyperbolic geometry. In the recent years, new and interesting connections between the two fields have emerged. Among them:

1. Recent developments in the study of 2-dimensional Cremona group, where infinite dimensional real-hyperbolic space serves a primary tool for analysis of group-theoretic properties of Cremona group. This breakthrough is a high point of a long chain of developments where hyperbolicity of the intersection form on the 2nd cohomology group is used in order to make geometric conclusions about algebraic surfaces.

2. Study of fundamental groups of Kaehler manifolds. Here hyperbolic geometry appears in both differential-geometric and metric form, where group actions on real-hyperbolic spaces, trees and Gromov-hyperbolic spaces serve as an important tool for studying both fundamental groups and geometric structure of compact Kaehler manifolds. Furthermore, real-hyperbolic geometry appeared as a tool in constructing complex-projective varieties with prescribed fundamental groups.

3. Interesting connections and similarities between geometry of hyperbolic manifolds and geometric decompositions of 3-dimensional manifolds on one hand and study of projective varieties along the lines of the minimal model program.

4. Geometry of the compact quotients of complex balls, where algebraic and number-theoretic properties of lattices in PU(n,1) are reflected in algebro-geometric properties of the ball quotients.

These and possibly other related topics will be in the focus of the conference.

Lectures

## Confirmed Speakers

Benoît Claudon (Université de Lorraine, France)
Alexandre Ananin (Unicamp, Brazil)
Nicolas Bergeron (Paris 6, France)
Luca Di Cerbo (Duke University, USA)
Ted Chinburg (University of Pennsylvania, USA)
David Dumas (UIC, USA)
Jun-Muk Hwang (KIAS, South Corea)
Stéphane Lamy (Toulouse, France)
Dmitri Panov (King’s College London, UK)
Julien Paupert (Arizona State University, USA)
Jorge Vitório Pereira (IMPA, Brazil)
Pierre Py (Université de Strasbourg, France)
Nicholas Shepherd-Barron (University of Cambridge, UK)
Peter Shalen (UIC, USA)
Matthew Stover (University of Michigan, USA)
Domingo Toledo (University of Utah, USA)

List

## Organizing Committee

C. Araujo (IMPA, Brazil)
M. Belolipetsky (IMPA, Brazil)
M. Kapovich (UC Davis, USA)
J. Kollár (Princeton University, USA)

Program

## Registration

 Category Prices Students (Master/Ph.D) US$40.00 R$ 80.00 Researchers US$80.00 R$ 160.00

## Venue: Hotel La Plage, Cabo Frio, Brazil

WebPage

Postal Address: Instituto Nacional de Matemática Pura e Aplicada
Estrada Dona Castorina 110, Jardim Botânico
Rio de Janeiro, RJ, CEP 22460-320, Brasil
E-mail: eventos@impa.br