Services aux conférences Mandl

Résumé: This workshop is to bring together mathematicians working in algebraic geometry and topology, mathematical physics, representation theory in order to exchange results, questions and points of view on the role of triangulated categories in their respective fields.

Résumé: The workshop is planned to coincide with the 80th birthday on April 22, 2009 of Sir Michael Atiyah PRS, PRSE, Fields and Abel Medallist, and undoubtedly the most influential British mathematician of the last 50 years. Perhaps the most exciting interaction between physics and mathematics at the moment is in Quantum Field Theory and String Theory. The proposed workshop is intended to bring the world leaders in this interaction to Edinburgh; to exchange ideas, to give lectures to active practitioners in the fields and to announce their latest results.

Résumé: In the 1980's Grothendieck formulated his anabelian conjectures that brought to an hitherto-unexplored depth the interaction between topology and arithmetic. This suggested that the study of non-abelian fundamental groups could lead to a new understanding of deep arithmetic phenomena, including the arithmetic theory of moduli and Diophantine finiteness on hyperbolic curves. A certain amount of work in recent years linking fundamental groups to Diophantine geometry intimates deep and mysterious connections to the theory of motives and Iwasawa theory, with their links with arithmetic problems on special values of L-functions such as the conjecture of Birch and Swinnerton-Dyer. The goal of this programme is to investigate the ideas and problems of anabelian geometry within the global context of mainstream arithmetic geometry.