MATHEMATICS
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There is a one-to-one correspondence between nondegenerate set theoretical solutions of the Yang-Baxter equation and algebraic structures called biracks. On the other hand, biracks play an important role in knot theory. Biracks are algebras which have a structure of two one-sided quasigroups and sa…
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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 partial…
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My area of expertise is probability theory.
Strand 1. Applications of probabilistic, algebraic and analytic methods in modern mathematical statistics, especially in graphical models. In particular, I study the problem of model selection for so-called colored graphical models.
Strand 2. The s…
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My research focuses on probability theory and its noncommutative generalization - the so-called free probability.
Noncommutative probability naturally arises when considering large independent random matrices, hence my interest in random matrix theory. Large random matrices in the limit converge …
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Discrete optimisation
Discrete optimisation algorithms design and complexity analysis
Generating and counting combinatorial objects
Modeling practical problems such as resource allocation, goods divisions, job scheduling, program verification, cybersecurity with logic programs and mixedi…
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partial differential equations and their applications, qualitative analysis of solutions of partial diffrential equations
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My research focuses on analysis on metric measure spaces. In particular I study Sobolev spaces and the relationship between Sobolev's inequality and the geometry of metric space. Moreover, I study function spaces, with particular amphasis on the structure of relatively compact subsets.
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