Chamsol Park's homepage
About
I am a J.J. Sylvester Assistant Professor (postdoctoral position) in Department of Mathematics at Johns Hopkins University. My Postdoc Advisor is Professor Christopher D. Sogge. In May 2022, I received my PhD degree in Mathematics from the University of New Mexico under the supervision of Professor Matthew D. Blair. Before I came to UNM, I received a Bachelor's degree in Mathematics Education at the Korea National University of Education. Here is my CV.
I am interested in harmonic analysis and its interactions with partial differential equations, such as the Helmholtz equation and wave equation on compact Riemannian manifolds. Specifically, I am interested in L^p estimates on restrictions of the eigenfunctions of the Laplace-Beltrami operators on compact Riemannian manifolds.
The main idea for my work so far is to convert eigenfunction estimate problems into oscillatory integral operator problems by using the Lax parametrix and/or Hadamard parametrix on compact Riemannian manifolds (or, on their universal covers in the presence of nonpositive sectional curvatures, making use of the Cartan-Hadamard theorem). Once we have oscillatory integral operators in our hands, we can think about machineries, such as, Young's inequality, Hormander's theorem, and/or oscillatory integral estimates related with fold singularities of the canonical relations, and so on.
The list of preprints is as follows:
Eigenfunctions restriction estimates for curves with nonvanishing geodesic curvatures in compact Riemannian surfaces with nonpositive curvature (available in arXiv: http://arxiv.org/abs/2112.04371)
Restriction of Schrodinger operators on compact Riemannian manifolds with singular potentials (in preparation, with Matthew Blair)