Cohomological Methods in the Theory of Algebraic Groups 31 August – 4 September  2015

In the last 15 years, the theory of algebraic groups has witnessed an ever increasing use of cohomological methods from modern algebraic geometry and algebraic topology. These new methods have led to breakthroughs in a number of classical problems in algebra, which seemed beyond the reach of earlier purely algebraic techniques. The most famous example is Voevodsky’s development of techniques from homotopy and cobordism theory in the context of motivic categories (containing schemes), which have resulted first in the solution of the Milnor conjecture and then of the more general Bloch-Kato conjecture. Another striking example of this ongoing trend is Panin and Fedorov’s proof of the Grothendieck-Serre conjecture on rationally trivial torsors in the geometric case. The purpose of this workshop is to provide a forum for experts in the field of algebraic groups or in related areas to exchange ideas, disseminate new techniques and discuss recent developments. The workshop will be an opportunity for younger researchers to learn about open problems and state of the art techniques in this field. The conference will also be a good occasion for congratulating A. S. Merkurjev on his 60th birthday.
Scientific & Organizing Committee Baptiste Calmes (Université d’Artois) Vladimir Chernousov (University of Alberta) Nikita Karpenko (University of Alberta) Speakers The spectrum of the equivariant stable homotopy category Embeddings of maximal tori in classical groups and explicit Brauer-Manin obstruction Motivic decompositions of varieties of unseparated flags after Srinivasan Troisième groupe de cohomologie non ramifiée et variétés rationnellement connexes Cohomologie non abélienne non ramifiée Semisimple stably Cayley groups The rational motivic sphere spectrum and motivic Serre finiteness
  • Ivan Panin (Steklov Institute of Mathematics, St Petersburg)
On the Grothendieck–Serre conjecture concerning principal G-bundles over reductive group schemes A Hasse principle for simply connected groups over function fields of p-adic curves On examples of varieties that are not stably rational Arason Invariant for orthogonal involutions The rationality problem for forms of moduli spaces of stable marked curves Division algebras and separable subfields
  • Alexander Sivatski (University ‘Federal do Ceara’)
The principal results of Alexander Merkurjev on central simple algebras over fields (survey) The group K_2 of a biquaternion algebra Outer automorphisms of algebraic groups Decomposition of the diagonal, and applications Subtle Stiefel-Whitney classes and the J-invariant of quadrics