## University of Sydney Algebra Seminar

# Daniel Juteau (Universit\'e de Caen)

## Friday 25th October, 2:35-3:35pm, Carslaw 351

### Parity sheaves

In joint work with Carl Mautner and Geordie Williamson, we introduced parity sheaves which are a nice substitute for intersection cohomology sheaves when one uses coefficients in positive characteristic. This class is preserved by direct images along proper and "even" morphisms. We will see how intersection forms control the decomposition of such a direct image (this is a weak substitute for the decomposition theorem). In the setting of flag varieties and Bott-Samelson resolutions, those forms can be computed using the Soergel calculus of Elias-Williamson, which is being explained in Williamson's lecture series.