The author observes that certain numbers occurring in Schubert calculus for $\text {SL} _n $
also occur as entries in intersection forms controlling decompositions of Soergel bimodules …

Given a scheme in characteristic p together with a lifting modulo p 2, we construct a functor
from a category of suitably nilpotent modules with connection to the category of Higgs …

We prove most of Lusztig's conjectures on the canonical basis in homology of a Springer
fiber. The conjectures predict that this basis controls numerics of representations of the Lie …

R.–Dans cet article nous construisons et étudions une action du groupe de tresses affine
associé à un groupe algébrique semi-simple sur les catégories dérivées de faisceaux …

Given a certain kind of linear representation of a reductive group, referred to as a quasi-
symmetric representation in recent work of Špenko and Van den Bergh, we construct …

We prove that the canonical dimension of a coadmissible representation of a semisimple p-
adic Lie group in a p-adic Banach space is either zero or at least half the dimension of a …

These are notes for a course given at Princeton University in Fall 2022. The goal of this
course is to ultimately explain some work in progress of the author with Jacob Lurie on …

Springer resolution of the set of nilpotent elements in a semisimple Lie algebra plays a
central role in geometric representation theory. A new structure on this variety has arisen in …

We study Lie algebroids in positive characteristic and moduli spaces of their modules. In
particular, we show a Langton's type theorem for the corresponding moduli spaces. We …

In this paper we construct an action of the affine Hecke category (in its 'Soergel bimodules'
incarnation) on the principal block of representations of a simply connected semisimple …