Positivity, coherent sheaves, and representation theory

by Dr Pramod Achar (Louisiana State University, USA)

Tuesday 3 Aug 2010, 16:00 → 17:00 Asia/Kolkata

Maths. Seminar Room A-369 (Colaba Campus)

A number of questions in representation theory involve an endomorphism algebra endowed with a natural Z-grading; sometimes, deep consequences follow if it can be shown that the negative-degree components vanish. I will explain several instances of such `positivity phenomena' in derived categories of coherent sheaves, following work of Arkhipov, Bezrukavnikov, Ginzburg, and others. I will then discuss a new approach to proving positivity theorems, followed by some potential applications.