Thorge Jenssen : The ABC of p-Cells

The Hecke category is a categorification of the Hecke algebra
that plays an important role in (geometric) representation theory. Using this categorification, I will introduce a positive characteristic analogue of the famous Kazhdan-Lusztig basis of the Hecke algebra, called the p-canonical or p-Kazhdan-Lusztig basis. If time permits, I will mention connections between the p-Kazhdan-Lusztig basis and the representation theory of reductive algebraic groups.
Motivated by the very rich theory of Kazhdan-Lusztig cells,
I study cells with respect to the p-Kazhdan-Lusztig basis.
Throughout the talk, I will use SL_2 as a running example. In the end, I will give a complete description of p-Cells in finite type A and mention some interesting results in finite types B and C.