Title: Revisit to eigenfunction estimates restricted to a curve with nonvanishing curvatures

Abstract: In this talk, we want to discuss eigenfunction estimates restricted to a curve with nonvanishing curvatures in a compact Riemannian manifold. When we study the wave equation on a compact Riemannian manifold, considering eigenfunctions of the Laplace-Beltrami operator in the manifold is helpful, since the eigenfunctions multiplied by some exponential functions are solutions to the wave equation. Restriction estimates of them on a general curve have also been studied so far. We will review the theorem that we can improve the estimates when the general curve is replaced by a curve with nonvanishing geodesic curvature, and will talk about how the previous theorem can help us to consider the logarithmic improved estimates when we further assume nonpositive sectional curvatures in the manifold.

About the Speaker: Chamsol Park is a sixth year graduate student at UNM who is working under the direction of Professor Matt Blair. Chamsol graduated from the Korea National University of Education, and his major was Education of Mathematics. He received silver prizes twice in the Mathematic Competition for University in Korea.