The linkage principle says that the category of representations
of a reductive group GG in positive characteristic
decomposes into "blocks" controlled by the affine Weyl group. We
will discuss the beautiful geometric proof of this result that
Simon...
Smith theory is a type of equivariant localization with respect
to a cyclic group of prime order pp, with coefficients in a
field of the same characteristic pp. It has been the source of
various recent advances in modular representation theory and...
The talk is about convolution in the setting of geometric
representation theory. What are its formal properties? As a
starting point, let G be a group and let D(G) be the derived
category of constructible sheaves on it. Convolution turns D(G)
into a...
Motivated by a formal similarity between the Hard Lefschetz
theorem and the geometric Satake equivalence we study vector spaces
that are graded by a weight lattice and are endowed with linear
operators in simple root directions. We allow field...
Before the "geometric Satake equivalence" there was a
decategorified version of it which however contained most of its
essential features. In my talk I will talk about some of the ideas
which have led to this theory. In particular I will explain
the...
This talk will be an exposition of a recent paper of
Bezrukavnikov-Gaitsgory-Mirkovic-Riche-Rider giving an
Iwahori-Whittaker model for the Satake category. The main point is
that their argument works for modular coefficients. I will give
some...
This is the third talk in a series of three talks on the derived
Satake equivalence. I will give an overview of the article of
Bezrukavnikov and Finkelberg which explains how the equivariant
derived category of the affine Grassmannian can be...
This is the second talk in a series of three talks on the
derived Satake. I will give an overview of an article by Ginzburg
which laid the foundational ideas for this equivalence.
(Equivariant) Cohomology of the affine Grassmannian and
Ginzburg’s picture
This is the second talk in a series of three talks on the
derived Satake. I will give an overview of an article by Ginzburg
which laid the foundational ideas for this...
This is the first talk in a series of three talks towards
understanding Bezrukavnikov-Finkelberg's derived geometric Satake
equivalence. In this talk, we recall the geometry of equal
characteristic affine Grassmannians and some of the ingredients
of...
