Wykaz obszarów badawczych związanych z tagiem Kombinatoryka:
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| 1 |
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 to certain bounded operators on a Hilbert space. At the same time, elegant combinatorial structures such as lattices of non-crossing or interval partitions are used to describe free probability. On the other hand, analytic functions are used to describe the distribution. In summary, noncommutative probability uses a wide range of mathematical tools and interesting questions will be found in it for those interested in probability theory, combinatorics, functional analysis or complex analysis.
My research focuses on combinatorial aspects and connections with random matrices.
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| 2 |
My research interests concern mostly algorytmic graph theory: a field on the boundary of structural graph theory (considered a part of discrete mathematics) and design of algorithms (considered a part of theoretical computer science). A typical question I am trying to solve is: Given a computationally hard (usually graph) problem, does it become tractable, when the instances are restriced to a particular class?
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