About group
We are working to solve the current problems of the theory of orthomodular algebraic structures or optical properties of algebras and measurement theory built on these structures. These topics are motivated by quantum theory. We are one of the few teams in the world which combines the methods of functional analysis (continuous structure) and algebra and combinatorics (discrete structures) in the study of quantum mechanics. We achieve significant results touching several disciplines.
Purpose
The research results are in the study of the axiomatic foundations of quantum theory, in quantum measurement theory, in the quantum theory of measurement, quantum information theory and cybernetics.
Our Projects
- Measure theory on the von Neumann algebras (convergence theorem)
- Geometry of state spaces of C*-algebras and Jordan's algebras
- Specific logic (Dynkins systems)
- General quantum logic, compatibility, state space, noncommutative probability
- The construction of quantum logics
- Hilbert and Prehilbert spaces
- The independence of the optical properties of algebras in quantum field theory
Our Funding
Our research is continuously funded by various grants for basic and applied research including:
- Quantum logic as orthomodular structure, the Grant agency of the CZECH republic 201/93/0953, 1993-1995.
- The mathematical formalism of quantum theory, the Grant agency of the CZECH republic 201/96/0117, 1996-1998.
- Applied mathematics in engineering sciences, Research project of the MINISTRY of education of the CZECH republic MSM 210000010, 1999-2004.
- Operator algebras, ortokomplementární structures and noncommutative measure theory, the Grant agency of the CZECH republic 201/00/0331, 2000-2002.
- Noncommutative measure theory, the Grant agency of the CZECH republic 201/03/0455, 2003-2005.
- Applied mathematics in engineering and physical sciences Research project of the MINISTRY of education of the CZECH republic MSM 6840770010, 2005-2011.
- Algebraic and peacefully theoretical aspects of quantum structures, the Grant agency of the CZECH republic 201/07/1051, 2007-2009.
- Topological and geometric properties of Banach spaces and optical properties of algebras, the Grant agency of the CZECH republic P201/12/0290, 2012-2016.
