# Bounds for Restrictions of Laplace Eigenfunctions (17rit687)

## Organizers

(Stanford University)

(University of North Carolina at Chapel Hill)

(McGill University)

## Description

The Banff International Research Station will host the "Bounds for restrictions of Laplace eigenfunctions" workshop in Banff from October 15, 2017 to October 22, 2017.

In this workshop we plan to study the behavior of the $L^2$-mass of restricted Laplace eigenfunctions. We will be working on compact surfaces without boundary, and we will restrict the eigenfunctions to curves that are not a segment of a geodesic. We conjecture that the $L^2$-mass of the restrictions of quantum ergodic eigenfunctions to the curve $H$ are uniformly bounded above and below by a constant as the eigenvalue grows to infinity. Furthermore, the $L^2$-mass of any eigenfunctions to the curve $H$ have an exponential lower bound. Understanding these questions will have profound implications for the study of the nodal sets of eigenfunctions.

#### Bibliography

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).