Interactions between Algebraic Geometry and Noncommutative Algebra

Abstract

The workshop discussed the interactions between algebraic geometry and various areas of noncommutative algbebra including finite dimensional algebras, representation theory of algebras and noncommutative algebraic geometry. More than 45 mathematicians participated with a notable number of young mathematicians present. Mathematics Subject Classification (2000): 14A22, 16K20, 16S38, 16P90. Introduction by the Organisers This meeting had over 45 participants from 11 countries (Australia, Belgium, Canada, France, Germany, Italy, Israel, Norway, Russia, UK and the US) and 26 lectures were presented during the five day period. The sponsorship of the European Union allowed the organizers to invite and secure the participation of a number of young investigators. Some of these young mathematicians presented thirty minute lectures. As always, there was a substantial amount of mathematical activity outside the formal lecture sessions. This meeting explored the applications of ideas and techniques from algebraic geometry to noncommutative algebra . Several lecturers presented open problems to stimulate the interest of researchers in other areas. Areas covered include • noncommutative projective algebraic geometry, • Hopf algebras, • combinatorial ring theory, • symplectic reflection algebras, • representation theory of quivers and preprojective algebras • homological techniques and derived categories 1320 Oberwolfach Report 23/2006 The sweep of the meeting can be seen from de Jong’s contribution that uses contemporary algebraic geometry to prove a theorem in the classical theory of finite dimensional division algebras to the works of Keller-Reiten and Ingalls on cluster algebras. Additionally, de Jong notes a result obtained during the workshop with van den Bergh. Looking to the future, Goodearl and Zelmanov propose a number challenging problems. Zelmanov discusses both an interesting Lie algebra example and a possible connection to an old problem of Kurosh. The previous paragraph represents just a sampling of the scope and variety of the mathematics at the meeting. The abstracts following will give the whole story.