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Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

CIRM – Centre International de Rencontres Mathématiques

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

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.

Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics)

The Fields Institute for Research in Mathematical Sciences

This intensive graduate school will cover topics central to the Workshop on Interactions between Group Theory and Homotopy Theory the following week. This school is designed to give graduate students and early career researchers in related fields a better understanding of each subject, thus enabling the participants to better engage in the subsequent workshop.

Geometry and Topology,    Courses and Events for Math Students and Early Career Researchers

The Fields Institute for Research in Mathematical Sciences

Group theory and topology have a long and rich history of interaction. This workshop will bring together experts working on different aspects of this interaction in order to share ideas and boost the development of new methods that can be applied to the topology of configuration spaces, braid groups, mapping class groups and manifolds, and spaces of commuting elements.

Geometry and Topology,    Courses and Events for Math Students and Early Career Researchers

Banach Center

Since its origins in the work of Sophus Lie (now more than a century ago), Lie theory has seen tremendous developments and is now fundamental in many areas of mathematics (like group theory, geometry, symmetric spaces etc) and physics (quantum mechanics, particle physics, theory of gravity). Nowadays there are specialized computer packages such as LiE, the Atlas project, the package Chevie for GAP3, the program ChevLie. Also the more general purpose computer algebra systems GAP4, MAGMA and SageMath have large libraries for dealing with various objects that are central to Lie theory.