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 measures)
- 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 bi-holomorphic mappings, generalization of the Cauchy-Riemann problem)
- Mathematical analysis (theory of polynomial maps, splines, differentiation theory, pseudodistribution theory, function inequalities)
- Mathematical physics (space-time singularities, geometric properties of quantum groups)
- Number theory (polynomials over general fields, zeta and L-functions, analytic and p-adic methods, elementary number theory)
- Numerical analysis (numerical methods in partial differential equations, approximation of spectra of linear operators, ill-posed 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, dimension theory).
