Configuration spaces of points and their homotopy type

Abstract: Given a topological space X, one can study the configuration space of n points on it: the subspace of X^n in which two points cannot share the same position. Despite their apparent simplicity such configuration spaces are remarkably complicated; the homology of these spaces is reasonably unknown, let alone their homotopy type. This classical problem in algebraic topology has much impact in more modern mathematics, namely in understanding how manifolds can embed in other manifolds, such as in knot theory. In this talk I will give a gentle introduction to this topic and explain how using ideas going back to Kontsevich we can obtain algebraic models for the rational homotopy type of configuration spaces of points.

mathematical physicsalgebraic geometryalgebraic topologydifferential geometryrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry and Physics @ Lisbon