EVENT DETAILS AND ABSTRACT

Title: Low-frequency generalized period integrals of eigenfunctions
Speaker: Emmett Wyman
Speaker Info:
Brief Description:
Special Note:
Abstract:

Let $e_\lambda$ be an $L^2$-normalized eigenfunction on a compact surface $M$ with Laplace eigenvalue $-\lambda^2$. By a period integral, we mean an integral of the eigenfunction $e_\lambda$ along some fixed closed curve $\gamma$ in $M$. The question of when period integrals satisfy better-than general bounds is related to the classical dynamics of the geodesic flow, and hence the global geometry of $M$ and $\gamma$. Here, we discuss generalized period integrals, which are precisely the Fourier coefficients of the restriction of $e_\lambda$ along $\gamma$. We give a brief overview on what is currently known about the bounds on generalized periods over curves in surfaces, and sketch how the improvements to these bounds connect to the classical dynamics on $M$.