Professor Alexander Sobolev, PhD

Room 710
Tel:- 020-7679-2863
E-mail:- a.sobolevucl.ac.uk
Fax: 020-7383-5519

Research Interests
Spectral Theory, Differential Operators, Geometry of Numbers

Alex Sobolev's  research area is spectral theory of partial differential operators. Current research is focused on proper ties of partial differential operators with periodic coefficients. A fascinating feature of periodic operators is the connection between their spectra and the properties of the underlying periodicity lattice.  This connection plays an important role in the proof of the famous conjecture due to H.Bethe and A. Sommerfeld, which states that the number of gaps in the spectrum is finite. Apart from analytic methods, the rigorous mathematical proof of this fact involves methods from Number
Theory, and geometry of numbers.