Professor, Doctor of Sciences

email: belishev@pdmi.ras.ru
PURE СПбГУ

Full-time job

St. Petersburg Department of V.A. Steklov Institute of Mathematics of the Russian Academy of Sciences, Laboratory of Mathematical Problems of Geophysics.

Specialization:

inverse problems of mathematical physics.
In particular, 

• multidimensional time-domain and frequency-domain coefficient inverse problems;
• reconstruction of Riemannian manifolds via the boundary data;
• inverse problems for the vectorial dynamical systems;
• forward and inverse problems on graphs;
• mathematical control theory problems.

 Directions of research

• inverse problem theory;
• control and system theory;
• partial differential equations;
• asymptotic methods in mathematical physics;
• function analysis and operator theory.

Prospective goals:

• relations between inverse problems and C*-algebras and noncommutative geometry;
• function models of linear operators;
• inverse problems for multichannel dynamical systems.

Basic Research papers

1. Infringement of the condition for solvability of the converse problem for an inhomogeneous string
2. Boundary control in reconstruction of manifolds and metrics (the BC method)
3. Characterization of Data of the Dynamical Inverse Problem for a Two-Velocity System
4. Boundary Control Method and Inverse Problems of Wave Propagation
5. Boundary spectral inverse problem on a class of graphs (trees) by the BC method
6. Some remarks on the impedance tomography problem for 3d–manifolds.
7. Recent progress in the boundary control method
8. Dirichlet to Neumann operator on differential form
9. s-POINTS IN THREE-DIMENSIONAL ACOUSTICAL SCATTERING
10. A UNITARY INVARIANT OF A SEMI-BOUNDED OPERATOR IN RECONSTRUCTION OF MANIFOLDS
11. Elements of noncommutative geometry in inverse problems on manifolds