Wykaz obszarów badawczych:
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My scientific interests include universal algebra and lattice theory, with special focus on their applications in other areas of mathematics, for example:
- ordered structures, e.g. algebras with semi-lattice operation, power algebras, algebras of subalgebras, as well as convex subsets for partially ordered sets of various types;
- algebraic structures related to geometry, knot theory, and set-theoretical solutions to the Yang-Baxter equation, such as quandles, racks or biracks, and in a wider context: one-sided quasigroups;
- barycentric algebras (algebraization of real convex sets) and their applications, e.g. in the modelling of complex systems;
- closure lattices (lattices of subclasses, convexity lattices, congruence lattices etc.) and their complexity;
- classes of structures defined by identities and quasi-identities.
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Mathematics |