Colloquium February 6
Date: Friday, February 6
Time: 16:00 to 17:00
Place: 455 McBryde (Commons Room)
Speaker: Gunter Stolz of Univ of Alabama at Birmingham
Title: Bubbles tend to the boundary
Abstract: Consider the negative Dirichlet or Neumann Laplacian on a square. Add a potential perturbation which is supported on a small disk. How should the potential be placed in the square in order to minimize the lowest eigenvalue of the resulting Schrödinger operator? The answer to this question for the case of Neumann conditions is very different from the answer for the Dirichlet case. In particular, for the Neumann case the answer is independent of the sign of the potential. We will also discuss the optimal placement of infinitely many potential sites in a perturbed lattice. This can be applied to study the density of states of the random displacement model, a random Schrodinger operator which is used to model structural disorder.
Return to