Analysis and algebra with applications

The main topics of research are divided into four parts: (1) Complex analysis and applications: (a) Problems related to harmonic and HQC maps with applications (Thompson-Dirichlet) (b) Teichmuller theory and appl. (Compl. dynamics, String theory) (c) Theory of p-harmonic functions and theory of potentials (d) Applications of Compl. Analysis to graph theory (Coulson int. formula). (2) Functional analysis and applications: (a) Investigation of mutual relations between different classes and subclasses of regularly varying functions (b) Spectral theory problems for operators in real, compl. and quaternionic Banach and Hilbert sp. (c) Investigations of structures of spaces with nondeterministic distances and characterizations (analytical and topological) of convex sets and functions defined on these sp. (d) Investigations of existence of fixed points for mappings defined on spaces with nondeterministic distances and applications of acquired results in modern theories of physics. (3) Algebra and applications: (a) Methods of reduction of some linear systems of operator equat. (b) Some appl. of linear algebra to combinatorial enumeration, pseudo-inverses and graph theory (c) Some representations of some analytic functions (d) Some appl. of Groebner bases (e) Investigations of some properties of various types of graphs associated to rings (f) Some estimates related to the dimension and bases of spaces of matrices with rank conditions. (4) Riemann zeta function and related L-functions.