Kaitlynn N. Lilly

Hello! I am a second year Ph.D. student in the Applied Mathematics Department at the University of Washington advised by Tom Trogdon. I am broadly interested in numerical methods for partial differential equations (PDEs).

Specifically, I am developing a unified methodology integrating spectral theory, Riemann-Hilbert problems, and inverse scattering theory to efficiently derive, and numerically implement, transform pairs associated to time-evolution variable-coefficient PDEs. In particular, the approach combines analytical formulae with iterative ODE and Riemann-Hilbert methods to efficiently evaluate the forward and inverse transforms, giving a hybrid analytical-numerical method for such PDEs. The method has so far been demonstrated on transforms arising in the solution of the time-dependent Schrӧdinger and Dirac equations, producing an accurate and stable time evolution method that does not require time stepping.

Previously, I did a dual BS at University of Maryland, Baltimore County in Mathematics and Physics.