Configuration spaces. Geometry, combinatorics and topology Geometry, Combinatorics and Topology

These proceedings contain the contributions of some of the participants in the "intensive research period" held at the De Giorgi Research Center in Pisa, during the period May-June 2010. The central theme of this research period was the study of configuration spaces from various points of view. This topic originated from the intersection of several classical theories: Braid groups and related topics, configurations of vectors (of great importance in Lie theory and representation theory), arrangements of hyperplanes and of subspaces, combinatorics, singularity theory. Recently, however, configuration spaces have acquired independent interest and indeed the contributions in this volume go far beyond the above subjects, making it attractive to a large audience of mathematicians.

On the structure of spaces of commuting elements in compact Lie groups.- On the fundamental group of the complement of two real tangent conics and an arbitrary number of real tangent lines.- Intersection cohomology of a rank one local system on the complement of a hyperplane-like divisor.- Characters of fundamental groups of curve complements and orbifold pencils.- A survey of some recent results concerning polyhedral products.- Analytic continuation of a parametric polytope and wall-crossing.- Embeddings of braid groups into mapping class groups and their homology.- The cohomology of the braid group B3 and of SL2(Z) with coefficients in a geometric representation.- Pure braid groups are not residually free.- Hodge–Deligne equivariant polynomials and monodromy of hyperplane arrangements.- The contravariant form on singular vectors of a projective arrangement.- Fox–Neuwirth cell structures and the cohomology of symmetric groups.- Basic questions on Artin–Tits groups.- Rational cohomology of the real Coxeter toric variety of type A.- Arrangements stable under the Coxeter groups.- Quantum and homological representations of braid groups.- Cohomology of the complement to an elliptic arrangement.- Residual nilpotence for generalizations of pure braid groups.- Some topological problems on the configuration spaces of Artin and Coxeter groups.- Chromatic quasisymmetric functions and Hessenberg varieties.- Geometric and homological finiteness in free abelian covers.- Minimal stratifications for line arrangements and positive homogeneous presentations for fundamental groups.