Organization board: Sébastien Boucksom, Yann Rollin, Carl Tipler
Scientific board: Claudio Arezzo, Olivier Biquard, Paul Gauduchon, Michael Singer
Kähler geometry is a very active research field, at the crossroads between algebraic and Riemannian geometry. Important breakthrough, that lead to solve the Yau-Tian-Donaldson conjecture in the Fano case, have been achieved recently. A spring school involving mini-lectures and talks around this thread of new ideas in Kähler geometry is organized at Nantes University. The goal of the school is to develop certain technical skills, useful to address a variety of important questions in algebraic geometry and global analysis on manifolds, aimed for PhD students and young researchers. Geometric flows, like the Kähler-Ricci flow for instance, and the associated quantification by the Donaldson dynamical system, will be among the essential tools dealt with during the school.
Conference - Teichmüller Theory in Higher Dimension and Mirror Symmetry
Organization board: Yves Coudène, François Maucourant, Françoise Pène, Barbara Schapira, Samuel Tapie
Scientific board: Jon Aaronson, Jean-Pierre Conze, Gilles Courtois, Domokos Szasz
This conference will focus on dynamical systems which naturally preserve a measure with infinite mass. These systems appear in a geometric or probabilistic context, or may come from natural sciences. When the invariant measure has infinite mass, recurrence is no longer automatic, usual mixing properties disappear and new asymptotical properties (such as rationnal ergodicity) may occur. Such systems may develop various and subtil behaviours, which could not exists in finite measure dynamics.
This conference will gather international experts on this topic, and will allow young researcher to have an easy access to the large recent developpment on such questions.
Conference - Dynamics of algebraic transformations
Scientific board: Bachir Bekka, Emmanuel Breuillard, Nizar Demni, Alex Lubotzky
The conference deals with themes around random walks on algebraic structures.
Dynamical sytems on groups, homogeneous spaces, and related structures (graphs, quantum groups , groupoids,...) are rich objects, involving various fields of mathematics (probability, group theory, topology, number theory, operator algebras, Banach space geometry, etc). They are also useful as modelling tools for other sciences (physics, computer science, economics, etc); for instance, expander graphs, which are of interest in theoretical computer science, are graphs for which the associated random walk has special spectral properties and their explicit construction involves sophisticated tools such as Kazhdan's property (T) or Selberg's inequality.
The conference aims to give a flavor of the various aspects of the subject by bringing together some experts with major contributions to the field.
This conference will also be the opportunity to celebrate the 80th birthday of Yves Guivarc'h, who played a major part
in the development of probability on algebraic and geometric structures, a subject with an ever growing interest for the last 30 years.