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CIRM – Centre International de Rencontres Mathématiques

CIRM – Centre International de Rencontres Mathématiques

During the past decades, Teichmüller–Thurston theory and its connections to geometrization of 3-manifolds have been used as a model to understand discrete subgroups of higher rank Lie groups and their associated locally homogeneous manifolds. This lead to spectacular developments in which the notion of Anosov group (a subtle higher rank generalization of convex-cocompactness) plays a central role. This school, aimed primarily at PhD students and young postdocs, will present the fundamental results on which these recent developments build, including both geometric, dynamical and analytic aspects of discrete subgroups of Lie groups.

CIRM – Centre International de Rencontres Mathématiques

This workshop will bring together experts in Algebraic Geometry to discuss and try to solve problems that are relevant to the classification of finite subgroups of Cremona groups up to conjugation. Priority would be given to the following four related areas: automorphisms of Fano varieties, classification of Fano varieties with prescribed symmetry groups, rationality problems for Fano varieties over algebraically non-closed fields, and K-stability of Fano varieties, with a special focus on the real Cremona groups.

CIRM – Centre International de Rencontres Mathématiques

Symmetries of the plane/space given by rational functions come with the basic mathematical structure of a group. This group, known as the plane/space Cremona group, is huge. One way to understand this group better is to classify all its finite subgroups. For the plane Cremona group, this was done Igor Dolgachev, Jeremy Blanc and Vasily Iskovskikh two decades ago, who classified finite subgroups of the plane Cremona group up to isomorphism. We intend to obtain some progress in this direction for the space Cremona group (real and complex), which is a much more difficult task.