Braxton Osting, braxton@math.ucla.edu
Co-authors: Jeremy Marzuola
Concentrated density of states and the triangular lattice
Motivated by a problem in solar cell design, we consider a spectral optimization problem for a weighted graph
Laplacian on a geometric configuration of points, where the edge weights are dependent on pairwise distances.
We seek finite (infinite) configurations of points whose associated Laplacian has eigenvalues (density of states)
concentrated at a particular value. The challenge of this problem stems from the geometric constraints on the
point configuration. Preliminary results show that for the two-dimensional periodic problem, the triangular lattice is a robust optimizer of this and several other spectral properties. This is joint work with Jeremy Marzuola.