Dr Andrew J. Horning of MIT with a seminar at NASK
Join us for a seminar on computing spectral properties of infinite-dimensional operators. On Wednesday, June 28, at 3:30 pm, Andrew J. Horning, Ph.D., of MIT’s Department of Mathematics will present the key computational challenges posed by infinite-dimensional spectral problems.
Using examples and SpecSolve, he will present ways to deal with these challenges.
Ever since Joseph Fourier used sines and cosines to diagonalize the Laplacian and solve the heat equation in 1822, spectral decompositions of linear operators have empowered scientists to disentangle complex physical phenomena. For example, eigenvalues and eigenvectors play a key role in analyzing the performance of microelectromechanical (MEM) resonators, the allowed energy states of quantum devices, and the controllability of certain dynamical systems. In many applications, the linear operator is a differential or integral operator that acts on an infinite-dimensional space of functions. In this talk, we outline the key computational challenges posed by infinite-dimensional spectral problems and present a rigorous framework based on the resolvent operator to tackle them. We proceed in a tutorial style and illustrate each idea and algorithm with an example from the public software repository SpecSolve in Matlab.
The seminar will be held in an online format, in English, with a possibility to discuss and pose questions to our guest. Those wishing to participate in this event can contact us at wsparcie_nauka@nask.pl