We calculate the dg algebra of global functions on commuting stacks of complex reductive
groups using tools from Betti Geometric Langlands. In particular, we prove that the ring of …

For a complex reductive group, we construct a semi-orthogonal decomposition of the
cocenter of the universal variant of its affine Hecke category. We use this to calculate the …

Let GG be an affine algebraic group defined over a field kk of characteristic 0. We study the
derived moduli space of GG‐local systems on a pointed connected CW complex XX …

In this paper, we define and study derived character maps of finite-dimensional
representations of homotopy simplicial groups, which are homotopy algebras over the …

Symmetric homology is a natural generalization of cyclic homology, in which symmetric
groups play the role of cyclic groups. In the case of associative algebras, the symmetric …

We study the question for which commutative ring spectra $ A $ the tensor of a simplicial set
$ X $ with $ A $, $ X\otimes A $, is a stable invariant in the sense that it depends only on the …

We define and study (derived) character maps of finite-dimensional representations of∞–
groups. As models for∞–groups we take homotopy simplicial groups, ie the homotopy …

We develop a spectral sequence for the homotopy groups of Loday constructions with
respect to twisted cartesian products in the case where the group involved is discrete. We …

This thesis investigates some geometric properties of representation schemes of associative
unital algebras, broadly speaking schemes whose geometric points correspond to …

In this paper we propose a procedure for a noncommutative derived Poisson reduction, in
the spirit of the Kontsevich-Rosenberg principle:" a noncommutative structure of some kind …