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.
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, to appear in Annales Henri Poincaré.
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. Download an MP4 video, showing the dynamics of eigenvalues and bounds as a parameter changes.
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.
- e.: M.Levitin@reading.ac.uk
- t.: (+44)(0)(118) 378 8997
- f.: (+44)(0)(118) 931 3423
- a.: Whiteknights, PO Box 220, Reading RG6 6AX, United Kingdom
- office: 3.03
- with E B Davies, Spectra of a class of non-self-adjoint matrices
- with R J Downes and D Vassiliev, Spectral asymmetry of the massless Dirac operator on a 3-torus
- with D M Elton and I Polterovich, Eigenvalues of a one-dimensional Dirac operator pencil
- Analysis of PDEs, Symposium in honour of Vladimir Maz'ya, Liverpool, 16-17 December 2013
- Spectral Theory of Laplace and Schroedinger Operators at Banff, July 28 - August 2, 2013