Ricardo Campos: A graph model for configuration spaces of points on a manifold.

ABSTRACT:  Given a manifold M, one can study the configuration space of n points on the manifold, which is the subspace of \(M^n\) in which two points cannot be in the same position. The study of these spaces is of interest in areas such as algebraic topology, rational homotopy theory or quantum field theory. Despite the apparent simplicity, even the homology of these spaces is reasonably unknown, let alone their (rational/real) homotopy type. In this talk, I will present a complex of graphs that models these spaces and, under certain conditions, takes into account a natural right \(E_D\) operadic module structure.

This is joint work with Thomas Willwacher based on arXiv:1604.02043 .