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Scientific activities

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
  • set-theoretical  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 bi-holomorphic 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

Instytut Matematyki Wydział FTIMS Politechnika Łódzka, 90-924 Łódź, ul. Wólczańska 215, tel. 42 631-36-17, fax. 42 631-38-65