Sergio Zamora, Max Planck Institute for Mathematics in Bonn

Title: The lower semi-continuity of a fundamental group and nilpotent structures in persistence.

Abstract: When a sequence of compact geodesic spaces X_i converges to a compact geodesic space X, under minimal assumptions there are surjective morphisms π₁(X_i) → π₁(X) for i large enough. In particular, a limit of simply connected spaces is simply connected. This is clearly not true for non-compact limits as one can see from a sequence of ellipsoids converging to a cylinder. We study how symmetries can allow one to study this lower semi-continuity of π₁ in the non-compact case, and how nilpotent structures naturally arise in this context.