12 January - 26 June 2009

**Organisers:** Professor M Geck *(Aberdeen)*, Professor A Kleshchev *(Oregon)* and Professor G Röhrle *(Ruhr-Universität Bochum)*

Lie theory has profound connections to many areas of pure and applied
mathematics and mathematical physics. In the 1950s, the original "analytic"
theory was extended so that it also makes sense over arbitrary algebraically
closed fields, in particular, fields of positive characteristic.
Understanding fundamental objects such as Lie algebras, quantum groups,
reductive groups over finite or *p*-adic fields and Hecke algebras of various
kinds, as well as their representation theory, are the central themes of
"Algebraic Lie Theory".

A driving force has always been the abundance of challenging, yet very basic
problems, like finding explicit character formulae for representations. The
introduction of geometric methods (in the 1970s) has revolutionized the
field. It led to a flow of new ideas between several disciplines, and
produced spectacular advances. The ideas of "geometrization" and
"categorification" now play a fundamental role in the development of the
subject. New structures continue to arise from connections with other areas
of mathematics and mathematical physics, like the emerging theory of
*W*-algebras.

It is anticipated that the activities of the programme will lead to a focalisation and popularisation of the various recent methods, advances and applications of Algebraic Lie Theory.