I will talk about (relatively) recent ways to apply the affine Grassmannian as an algebro-geometric or topological object to representation theory of the reductive group in positive characteristic or quantum group at a root of unity.

Based on works (mostly in progress) with Boixeda Alvarez, McBreen, Yun, Shan, Vasserot

and Arinkin.

I will talk about (relatively) recent ways to apply the affine Grassmannian as an algebro-geometric or topological object to representation theory of the reductive group in positive characteristic or quantum group at a root of unity.

Based on works (mostly in progress) with Boixeda Alvarez, McBreen, Yun, Shan, Vasserot

and Arinkin.

I will talk about (relatively) recent ways to apply the affine Grassmannian as an algebro-geometric or topological object to representation theory of the reductive group in positive characteristic or quantum group at a root of unity.

Based on works (mostly in progress) with Boixeda Alvarez, McBreen, Yun, Shan, Vasserot

and Arinkin.

I will establish an equivalence between a block of the quantum category O at an odd root of unity and the heart of the "new" t-structure on a suitably singular affine Hecke category