The combinatorics of the Yang-Baxter equation
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MSCA-22-Vendramin01
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Beschrijving van het project
The research team investigates mathematical structures that are important in the study of the Yang-Baxter equation (YBE). Although the YBE has its origin in physics, it is now a fundamental mathematical object. The YBE plays a prominent role in several areas of mathematics, such as algebra and algebraic logic, combinatorics, geometry, topology and computer science.
The team contributes to the theory of algebraic structures related to the YBE. Among such algebraic structures, one finds skew braces, which are ring-theoretical objects that also appear in several areas of mathematics (e.g. regular subgroups, Hopf-Galois structures, flat manifolds, groups with exact factorizations, bijective 1-cocycles, nil and radical rings).
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Research Group ALgebra & ANalysis
ALAN investigates, by algebraic and anaytic means, mathematical theories and mathematical structures that are important in several basic areas of mathematics, such as approximation theory, functional analysis and topology, category theory, discrete geometry, algebraic geometry and differential geometry, number theory, probability theory and Lévy processes, symmetry, as incorporated by groups, quantum groups and their associated rings, algebras and representation theory.
These investigations are motivated by open classical problems as well as by the advent of exciting new areas of mathematics. Motivation also comes from outside mathematics, such as from computer science or physics, where mathematical structures that are studied are called upon as models.
The scope of the research has many connections with different central topics in mathematics and beyond. We list the main areas in which actively ongoing research is being done, together with the members presently involved.