Leonardo Patimo (University of Freiburg) Friday 28 February, 12-1pm, Place: Carslaw 275 Title: p-hybrid bases of the Hecke algebra Abstract: In the Hecke algebra of a Weyl group, for every parabolic subgroup one can define a hybrid basis that "interpolates" between the standard basis and the Kazhdan-Lusztig basis. Geometrically these bases can be obtained via hyperbolic localisation of perverse sheaves. We will see that in the modular setting we can obtain similar results using parity sheaves, leading to the construction of new p-hybrid bases with remarkable positivity properties. We will conclude by discussing some applications of these new bases. This is joint work with Thorge Jensen.