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English versionČeská verzeVerze pro tisk
Matematický ústav Akademie věd České republiky, v.v.i.

Research at the Institute

Research in the Institute is concerned mainly with mathematical analysis (differential equations, numerical analysis, functional analysis, theory of functions, mathematical physics), probability theory and mathematical statistics, mathematical logic, theoretical computer science and graph theory, numerical algebra, topology (general and algebraic), and theory of teaching mathematics. The Institute has six departments with research focused as follows:
  • Department of Evolution Differential Equations - General theory of evolution equations and qualitative properties of their solutions, in particular: theory of integro-differential equations of parabolic and hyperbolic type (equations with memory), mathematical models in fluid dynamics, Navier-Stokes equations, non-smooth and singular evolution problems, nonlinear conservation laws, long time behavior of solutions to equations of hyperbolic and parabolic type with weak dissipation, time-periodic processes, free boundary problems.
  • Department of Constructive Methods of Mathematical Analysis - Mathematical and numerical analysis by means of the finite element method of nonlinear physical phenomenons that are mathematically described by partial differential equations and inequalities of elliptic, parabolic or hyperbolic type.
  • Department of Topology and Functional Analysis- The operator theory in connection with the theory of Banach algebras and the function theory. General topology, functional analysis, Boolean algebras.
  • Department of Mathematical Logic, Numerical Algebra and Graph Theory - Mathematical logic, set theory, proof complexity, computational complexity, on-line algorithms, extremal combinatorial problems, theory of matrices, numerical algebra.
  • Branch in Brno - Algebraic topology, differential geometry, homological algebra, homological physics. Global properties of linear differential equations of higher order. Boundary value problems for functional differential equations and their systems. Asymptotic behaviours of solutions of differential equations. Partial differential equations of hyperbolic type. Differential equations in the Banach spaces. Qualitative theory of half-linear and quasi-linear differential/difference equations and dynamic equations on time scales.
  • Department of Didactics of Mathematics - Problems of mathematics education of students aged 5-15 years.

As part of reorganization the following two departments were dissolved in July 2010 and the researchers moved to other departments.

  • Department of Real and Probabilistic Analysis - Theory of Perron-type non-absolutely convergent integrals, theory of generalized differential equations, abstract integration theories, boundary value problems. Theory of stochastic equations in particular that of stochastic evolution equations. Development of multivariate and non-parametric statistical methods and their application in biology and in materials science, theory of random closed sets and their statistical testing (stereology).
  • Department of Qualitative Methods of Mathematical Analysis - The investigation of the structure of function spaces and of operators on these spaces. Application of the results to the solution of boundary value problems. Bifurcation, stability and continuation of solutions to variational inequalities and related problems, applications to problems in mechanics and to reaction-diffusion systems with (boundary or additional) conditions describing some regulation. Existence of solutions of static contact problems with Coulomb friction and dynamic contact problems formulated by the Signorini contact condition. Application of boundary integral equation method to mathematical physics.
For more information about the research in the Institute, see the english 2005 yearbook of the Institute (.pdf, 850KB).

Adresa: Matematický ústav AV ČR, v.v.i., Žitná 25, 115 67 Praha 1
Tel.: +420-222-090-711 (ústředna) Fax: +420-222-090-701 E-mail: mathinst@math.cas.cz