Applied Math Seminar: Nonlinear Eigenvalue Problems: Theory and Applications

Seminar | January 12 | 3:30-4:30 p.m. | 891 Evans Hall

 David Bindel, Cornell University

 Department of Mathematics

Vibrations are everywhere, and so are the eigenvalues that describe them. Physical models that include involve damping, delay, or radiation often lead to nonlinear eigenvalue problems, in which we seek complex values for which an (analytic) matrix-valued function is singular. In this talk, we show how to generalize eigenvalue localization results, such as Gershgorin's theorem, Bauer-Fike, and pseudospectral theorems, to the nonlinear case. We demonstrate the usefulness of our results on examples from delay differential equations and quantum resonances.