Previous Special Year Seminar
Geometric Satake equivalence: a historical survey
3:00pm|Simonyi Hall 101 and Remote Access
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...
Broue's Conjecture for $SL_2(\mathbb{F}_q)$ in defining
characteristic, predicts a derived equivalence between the
principal block of this group and the principal block of a Borel. A
structurally similar equivalence exist in the case of the...
No seminar: postponed to next week
Derived Equivalences for Blocks of Cyclic Defect
Iwahori-Whittaker category and geometric Casselman-Shalika
3:00pm|Simonyi Hall 101 and Remote Access
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...
Blocks and Defect Groups of SLn
The modular representation theory of a finite group naturally
breaks into different pieces called blocks, and the defect of a
block is a sort of measure of its complexity. I will recall some
basic aspects of this theory, and then give the complete...
The Derived Geometric Satake Equivalence of Bezrukavnikov and Finkelberg
3:00pm|Simonyi Hall 101 and Remote Access
This is the last talk towards understanding
Bezrukavnikov-Finkelberg's derived geometric Satake equivalence.
With the preparations from previous talks, we will introduce two
filtrations: a topological filtration on the equivariant cohomology
and an...
Decomposition numbers in defining characteristic
The decomposition of the reduction of a Deligne--Lusztig
character as a sum of Weyl modules is given by Jantzen's formula.
In the case of $SL_2(F_q)$ the formula can be proved by a direct
computation, and as a result we will see that the entries in...
