Starts 14 Jun 2017 15:00
Ends 14 Jun 2017 16:00
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Some Recent Estimates On Nodal Geometry In The High-Energy Limit
ICTP
Leonardo Building - Luigi Stasi Seminar Room
Abstract:
Given a closed manifold, the Laplace operator is known to possess a discrete spectrum of eigenvalues converging to infinity. We are interested in properties of the corresponding eigenfunctions as the eigenvalue becomes large (i.e. the high-energy limit). From a physical point of view, the eigenfunctions represent stationary states of a free quantum particle - when properly normalized, they may be interpreted as the probability density of a particle in the manifold. Various questions about the geometry of Laplace-eigenfunctions have been studied thoroughly - for example, distribution and measure of the vanishing (nodal) set; localization; shape and inner radius of nodal domains, etc. We present some recent results along these lines - this also includes joint work with M. Mukherjee.
Given a closed manifold, the Laplace operator is known to possess a discrete spectrum of eigenvalues converging to infinity. We are interested in properties of the corresponding eigenfunctions as the eigenvalue becomes large (i.e. the high-energy limit). From a physical point of view, the eigenfunctions represent stationary states of a free quantum particle - when properly normalized, they may be interpreted as the probability density of a particle in the manifold. Various questions about the geometry of Laplace-eigenfunctions have been studied thoroughly - for example, distribution and measure of the vanishing (nodal) set; localization; shape and inner radius of nodal domains, etc. We present some recent results along these lines - this also includes joint work with M. Mukherjee.