Periodic Reporting for period 4 - Loops and groups (Loops and groups: Geodesics, moduli spaces, and infinite discrete groups via string topology and homological stability)

The research project lies at the intersection of algebra, topology, and geometry, with the scientific goal of answering central questions about homological stability, geodesics on manifolds, and the moduli space of Riemann surfaces. Homological stability is a subject that has...