Speaker
Nilima Nigam, Simon Fraser University
Abstract
Spectral geometry relates properties of the spectrum of an operator to the geometric properties of the domain. In this talk we’ll survey some reformulations of elliptic eigenvalue problems – via integral operators, or in terms of Dirichlet-to-Neumann maps. These reformulations are then used to investigate the dependance of the spectrum on curvature and study spectral optimization. The reduction of the volumetric problem to a problem on the domain boundary leads to both computational efficiency and high accuracy for smooth curves. We’ll present these ideas in the concrete instance of the mixed Dirichlet-Neumann eigenvalue problem and the Steklov problem.
Nilima Nigam, Simon Fraser University
Abstract
Spectral geometry relates properties of the spectrum of an operator to the geometric properties of the domain. In this talk we’ll survey some reformulations of elliptic eigenvalue problems – via integral operators, or in terms of Dirichlet-to-Neumann maps. These reformulations are then used to investigate the dependance of the spectrum on curvature and study spectral optimization. The reduction of the volumetric problem to a problem on the domain boundary leads to both computational efficiency and high accuracy for smooth curves. We’ll present these ideas in the concrete instance of the mixed Dirichlet-Neumann eigenvalue problem and the Steklov problem.