# Marcel Rubió: Structure theorems for the cohomology jump loci of singularities

**Time: **
Wed 2019-11-13 13.15 - 15.00

**Location: **
Kräftriket, house 6, room 306

**Lecturer: **
Marcel Rubió, Stockholms universitet

### Abstract

In this talk we will take a closer look into the moduli spaces of rank one local systems. In the first part of the talk, I will introduce cohomology jump loci and its developments throughout the past years. This will include a detour to deformation theory; in particular, we will discuss Deligne's principle and its implications by Goldman-Millson and Simpson.

In the second part, we extend this framework to the \(L_\infty\) world, ultimately showing that for a complex algebraic variety with no weight-zero \(1\)-cohomology classes, the fundamental group is strongly restricted. The results we obtain are in contrast to the work by Simpson, Kapovich and Kollár, stating that every finitely presented group is the fundamental group of an irreducible complex algebraic variety with only normal crossings and Whitney umbrellas as singularities. This is joint work with Nero Budur.