levitin I am Professor of Applied Mathematics in the Department of Mathematics and Statistics, University of Reading.

I am always interested to hear from candidates for a PhD or a postdoctoral position.

Examples of some old and new research are below and elsewhere on this website.

Dirac eigenvalues The colour map shows the exact and asymptotic locations of the complex eigenvalues for 1d Dirac operator pencil wth a sign-indefinite potential, see D M Elton, M Levitin and I Polterovich, Eigenvalues of a one-dimensional Dirac operator pencil, arXiv:1303.2185, Annales Henri Poincaré.

eigenvalues The image shows real and complex eigenvalues, and their bound, of a linear indefinite pencil studied in E B Davies, M Levitin, Spectra of a class of non-self-adjoint matrices, arXiv:1311.6741, published in Linear Algebra and its Applications. Download an MP4 video, showing the dynamics of eigenvalues and bounds as a parameter changes.

isospectral The image shows two isospectral boundary value problems for the Laplacian on the half-circles which map into each other under the Dirichlet-Neumann boundary conditions swap, see the paper D Jakobson, M Levitin, N Nadirashvili, and I Polterovich, Spectral problems with mixed Dirichlet-Neumann boundary conditions: isospectrality and beyond, J. Comp. and Appl. Math. 194 (2006), 141-155.