About the Institute
Research
At present, research concentrates on the following disciplines:
 Algebra and algebraic geometry
(intersection theory and enumerative
geometry, vector bundles, characteristic classes, algebraic combinatorics,
noncommutative geometry, noncommutative algebra, classical algebra and
symmetric functions)

Differential equations and optimization (optimal control theory,
geometric and analytic properties of solutions of nonlinear
differential equations in mechanics and geometry, Sobolev spaces,
gravitation theory)
 Differential geometry (generalized manifolds and analytic geometric structures)
 Dynamical systems (iteration of mappings of intervals and holomorphic mappings, invariant m
easures)

Foundations and philosophy of mathematics (set theory, model theory,
set theory aspects of measure theory, computational complexity of
recursive functions)
 Functional analysis (Hilbert spaces,
geometry of Banach spaces, approximation theory, wavelets, operator
theory, topological algebras)
 Functions of a complex variable
(quasiconformal mappings, invariants of biholomorphic mappings,
generalization of the CauchyRiemann problem)
 Mathematical
analysis (theory of polynomial maps, splines, differentiation theory,
pseudodistribution theory, function inequalities)
 Mathematical physics (spacetime singularities, geometric properties of quantum groups)
 Number theory (polynomials over general fields, zeta and Lfunctions,
analytic and padic methods, elementary number theory)

Numerical analysis (numerical methods in partial differential
equations, approximation of spectra of linear operators, illposed
problems)
 Statistics
(theory of estimation, model selection, statistical models, decision
theory, testing statistical hypotheses.)
 Probability (stochastic analysis, stochastic control theory, stochastic processes,
applied probability)
 Topology (general topology, topology of metric compacta, infinite dimensional topology, di
mension theory).
Organization membership
Institute is a member of: