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, 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, published in Linear Algebra and its Applications. 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.
- with Yan-Long Fang and Dmitri Vassiliev, Spectral analysis of the Dirac operator on a 3-sphere
- with Rod Gover, Asma Hassannezhad and Dmitry Jakobson, Zero and negative eigenvalues of the conformal Laplacian
- with Marcelo Seri, Accumulation of complex eigenvalues of an indefinite Sturm-Liouville operator with a shifted Coulomb potential
- Dirichlet-to-Neumann Maps: Spectral Theory, Inverse Problems and Applications, CMO-BIRS Workshop, Oaxaca, Mexico