## University of Sydney Algebra Seminar

# Pramod Achar (Louisiana State University)

## Friday 3 June, 12:05-12:55pm, Carslaw 175

### Koszul duality and mixed geometry

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.