The Algebra Seminar next Friday 3 June will be given by Pramod Achar. --------------------------------------------------------------------------- Speaker: Pramod Achar (Louisiana State University) Date: Friday 3 June Time: 12.05-12.55pm Venue: Carslaw 175 Title: Koszul duality and mixed geometry Abstract: Since the seminal work of Beilinson-Ginzburg-Soergel in the mid-1990s, the phenomenon of Koszul duality -- a subtle kind of symmetry between simple modules and projective modules over a ring -- has played an important role in representation theory. A key example comes from the geometry of flag varieties, where one can see Koszul duality by looking at mixed perverse sheaves or mixed Hodge modules -- well, almost. I will explain Koszul duality and mixedness in elementary terms, and I will discuss what goes wrong with those mixed categories and (following Beilinson-Ginzburg-Soergel) how to fix them. I will also discuss more recent developments from joint work with S. Riche and S. Kitchen. ----------------------------------------------------------------------------