Spectral Theory Network  

Bristol The research of M. van den Berg is in the general area of spectral geometry with particular interests in the asymptotic behaviour of heat equation problems in regions with a nonsmooth boundary. The techniques are from stochastic analysis and PDE theory. A second area of research is a class of variational problems which occur in the theory of large deviations for random walks and the Wiener sausage. These variational problems are closely related to existence and uniqueness theorems for semilinear PDEs. The research of V. Liskevich is concerned with different aspects of the theory of second order elliptic and parabolic differential equations with measurable coefficients, $C_0$ semigroup theory (in particular Markov semigroups), Schrödinger semigroups, perturbation theory of linear operators, and the theory of Dirichlet forms. The research of Y. Netrusov is in the theory of spaces of weakly differentiable functions (Sobolev spaces, Besov spaces, LizorkinTriebel spaces) and applications, in particular to the eigenvalue distribution of Schrödinger operators and LiebThirring inequalities. 

