Simple closed curves on surfaces
2021 05 05
Moscow-Beijing Topology Seminar
The behaviour of simple closed curves on surfaces can reveal a great deal of geometric information about the underlying surface. We look at three theories within this theme, all pertaining to hyperbolic surfaces:
1. Birman and Series's geodesic sparsity theorem,
2. McShane and Rivin's simple length spectrum growth rate asymptotics (as well as later improvements by Mirzakhani), and
3. McShane identities.
I plan to give a feel for why these results hold, as well as my input in extending these results to more general types of surfaces.
Meeting ID: 831 5020 0580