30 apr 2015 -- 16:00
Aula Riunioni, DM, Pisa
Seminari di Algebra, Topologia e Combinatoria, Pisa
Although the ordinary representation theory of Lie algebras is extremely well developed, progress has been much slower in the modular case. A breakthrough was made twenty years ago when Premet proved a long-standing conjecture bounding the dimensions of modules. His techniques led to the discovery of finite W-algebras, and the latter theory has recently culminated in another milestone, showing that the bound mentioned before is best possible. I shall review the development of this theory and discuss some very recent results of mine regarding the structure theory of certain modular finite W-algebras.