# Past Representation Theory Seminar

We construct triangle equivalences between singularity categories of

two-dimensional cyclic quotient singularities and singularity categories of

a new class of finite dimensional local algebras, which we call Knörrer

invariant algebras. In the hypersurface case, we recover a special case of Knörrer’s equivalence for (stable) categories of matrix factorisations.

We’ll then explain how this led us to study Ringel duality for

certain (ultra strongly) quasi-hereditary algebras.

This is based on joint work with Joe Karmazyn.

The smooth representation theory of a p-adic reductive group G

with characteristic zero coefficients is very closely connected to the

module theory of its (pro-p) Iwahori-Hecke algebra H(G). In the modular

case, where the coefficients have characteristic p, this connection

breaks down to a large extent. I will first explain how this connection

can be reinstated by passing to a derived setting. It involves a certain

differential graded algebra whose zeroth cohomology is H(G). Then I will

report on a joint project with

R. Ollivier in which we analyze the higher cohomology groups of this dg

algebra for the group G = SL_2.

The smooth representation theory of a p-adic reductive group G with characteristic zero coefficients is very closely connected to the module theory of its (pro-p) Iwahori-Hecke algebra H(G). In the modular case, where the coefficients have characteristic p, this connection breaks down to a large extent. I will first explain how this connection can be reinstated by passing to a derived setting. It involves a certain differential graded algebra whose zeroth cohomology is H(G). Then I will report on a joint project with R. Ollivier in which we analyze the higher cohomology groups of this dg algebra for the group G = SL_2.