My research is on Difference Equations (via the Graph Laplacian), and Generalized Matrix Eigenvalues. The Graph Laplacian appears when discretizing PDEs using finite differences or finite elements (as a stiffness matrix). Frequently when it can be written down, the Eigenvector Matrix of the Graph Laplacian is a Vandermonde Type Matrix with eigenfunctions of the underlying PDE.
I enjoy making interactive visuals in Desmos / Matlab.