The Institute of Mathematics carries out research in the following areas:
1) Theoretical Mathematics:
 methods of set theory in real analysis, topology, theory of measure and integration
 classical descriptive set theory
 settheoretical topology
 infinite combinatorics
 proofs of consistency and independence
 real functions of one and several variables
 generalized convergence of sequences
 density topologies and their applications
 porous sets
 metric fixed point theory
 iterated systems of maps and fractals
 geometry of Banach spaces
 geometric properties of locally biholomorphic mappings
 differential geometry and topology
2) Applications of Mathematics in the Natural Sciences:
 optimization: methods based on duality theory of general equilibrium
 ordinary and partial differential equations and boundary value problems for these equations
 topological methods for nonlinear analysis
 dynamical systems, chaos, applications to mathematical modelling, kinetic models
 evolutionary equations and the theory of semigroups of operators
 infinite dimensional dynamical systems
 mathematical biology
3) Financial and Actuarial Mathematics:
 modeling of investment and insurance risks
 valuation of insurance companies
 management of assets and liabilities of insurance companies
 credibility theory and other methods of charging fees
 valuation of insurance reserves
 management of the risk of insolvency of insurance companies
 actuarial statistics
 modeling cycles in the financial markets
 portfolio management
 capital adequacy of insurance companies / investment firms
 optimal risk transfer
 ALM for pension plans
