University of Bath University of Bristol Imperial College London
University of Oxford Engineering and Physical Sciences Research Council The University of Warwick

Taught Course Centre

Spectral Theory of Partial Differential Operators

January - March 2012.  Professor A Laptev.

Hardy and Sobolev inequalities. Spectrum of Dirichlet and Neumann Laplacians.
Polya conjecture and Li and Yau inequalities.
Trace formulae, non-linear equations, solitons.
Discrete and continuous spectrum of Schrödinger operators.
Stability of matter. Bounds on the maximal negative ionisation of atoms.
Lieb-Thirring inequalities and their applications.
Spectrum of non-self-adjoint operators.
Spectral properties of differential operators on graphs.

More syllabi ]