### Friday Abstracts:

#### Nero Budur

Title: Homotopy of singular algebraic varieties

Abstract: By work of Simpson, Kollár, Kapovich, every finitely generated group can be the fundamental group of an irreducible complex algebraic variety with only normal crossings and Whitney umbrellas as singularities. In contrast, we show that if an irreducible complex algebraic variety has no weight zero 1-cohomology classes, then the fundamental group is strongly restricted: the irreducible components of the cohomology jump loci of rank one local systems containing the constant sheaf are complex affine tori. Work-in-progress with Marcel Rubió.

#### Ben Knudsen

Title: Homology of surface and graph braid groups

Abstract: I will present small chain complexes computing the homology of the unordered configuration spaces of a manifold and of a graph, respectively, which carry additional algebraic structures related to homological stability. I will present computations and describe the local-to-global techniques involved in the proofs.

#### Mario Salvetti

Title: Families of superelliptic curves and complex braid groups

Abstract: [joint work with F. Callegaro] We study the integral cohomology of the families \(E_n^d\) of superelliptic curves, consisting of \(d\)-fold coverings of the disc ramified over \(n\) distinct points. We find that \(E_n^d\) is the classifying space for the complex braid group of type \(B(d,d,n)\). This makes it possible to generalize some previous methods and perform new cohomological computations for such groups. In particular, we also investigate the stability properties of their cohomology.

#### Alexander Varchenko (cancelled)

Title: Solutions of KZ differential equations modulo \(p\)

Abstract: I will construct polynomial solutions of the KZ differential equations over a finite field \(F_p\) as analogs of hypergeometric solutions.

Uli Walther

Title: Equivariant D-modules (joint with Adnras Lorincz)

Abstract: Let G be an algebraic group acting on a complex variety X. We consider the strongly G-equivariant D-modules on X and study the categories they form. We discuss specifically the case when G acts on X with finitely many orbits. Then this setup defines a finite quiver. We determine these in the case of a spherical variety and show that they are representation finite.