Laboratory «Probability techniques in analysis» (10)

Planned project results:

Among the results of the project can be mentioned the following: unified approach to asymptotic estimates of planar orthogonal polynomials, new estimates of the integral mean spectrum, description of lattices generating various classes of Gabor frames, description of invariant Schrodinger operators for different configurations of point interactions, estimates on the rate of convergence in the central limit theorem for point and Pfaffian processes, Montgomery type estimates for the sine-process, description of tensor invariants for dynamical systems on symplectic manifold, studying the BBP transition in the Ising model, new estimates of asymptotic characteristics in multidimensional approximation, description of invariants of topological insulators, solution of the «Kerchief» problem, results on condenser approximation, new technique for the solution of the Delsart problem, estimates of the asymptotic design size, development of new methods in the balayage theory, conditions of universality of the limiting spectral distribution for Gram matrices.

Developing and implementing color correction algorithms for modern endoscopic systems used for diagnosis and treatment, building of a novel up-to date theoretical and methodological foundations to carry out the program of color processing of medical data; development and customization of multi-objective optimization schemes for problems of diagnosis and treatment for thrombotic events and complications.