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Research |
| Research areas |
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Operator algebras.
C*-algebras, Jordan algebras, states and weights (quantum measure theory),
subspace structures, independence of operator algebras, group
representations, applications to quantum field theory and mathematical
foundations of quantum theory.
(Jan Hamhalter, Martin Bohata, Veronika Sobotíková)
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Orthomodular structures (quantum logics).
Orthomodular posets, effect algebras, concrete (set-representable) logics,
logics with a symmetric difference, compatibility, states (measures),
pastings of logics, constructions of logics.
(Pavel Pták, Josef Tkadlec)
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Semigroups and groups.
Varieties of semigroups, various types of universality (categorial
universality, weak universality, Q-universality), subdirectly irreducible
semigroups in various varieties, partial representations of groups, Hamming
distances, Latin squares, Latin trades.
(Marie Demlová, Natalia Zhukavets)
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Algebras and superalgebras.
Lie, alternative, Malcev and their generalizations, Poisson and their
deformations.
(Natalia Zhukavets)
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Geometry of Banach spaces.
Differentiability of Lipschitz functions and mappings between Banach spaces,
porous and directionally porous sets in infinite dimensional spaces,
asymptotic convexity and smoothness.
(Jaroslav Tišer)
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Banach spaces.
Structure of separable and nonseparable Banach spaces, nonlinear functional
analysis, smoothness and renormings, polynomials in Banach spaces.
(Petr Hájek)
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Measure theory.
Covering and differentiation theorems in Hilbert space.
(Jaroslav Tišer)
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Coalgebraic methods in computer science.
Coalgebras as recursive specifications, iterative algebras and their
generalizations, semantics of infinite behaviour, algebras where every
recursive equation admits a strict solution, coequational presentations of
coalgebras, process algebra.
(Marie Demlová, Jiří Velebil)
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Interval probabilities, cooperative game theory and fuzzy logics.
Non-additive set functions with applications in game theory and interval
probabilities. Probabilistic models on MV-algebras.
(Tomáš Kroupa)
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Stochastic geometry.
Probabilistic modelling and statistical analysis of random geometrical
objects, point processes, random sets, MCMC simulations.
(Kateřina Staňková Helisová)
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