Doug Stryker dstryker at princeton dot edu
Index and intersection properties of the length spectrum
The length spectrum of a surface (introduced by Gromov) is a sequence of geometric invariants analogous to the Laplace spectrum. Just as each Laplace eigenvalue has an associated eigenfunction, each length spectrum invariant has an associated closed geodesic (proved by Chodosh and Mantoulidis). I will discuss joint work with Jared Marx-Kuo and Lorenzo Sarnataro investigating the geometric properties of these associated geodesics, including upper bounds on their Morse index and self-intersections.