21-11-2024
The Center of Mathematics and Applications (NOVA Math), promote the Seminar of Algebra and Logic with the title: “Transformation Semigroups and their Groups of Permutations: Transversal Properties”. Wolfram Bentz (Universidade Aberta and NOVA Math) is the speaker.
Abstract: In recent years, the interplay between permutations groups and transformations semigroups has lead to many interesting new results. In particular, the application of the classification of finite simple groups to problems in transformation semigroups paved the way for the exploration of new and interesting ideas, and it led to the production of impressive mathematics involving combinatorics, automata theory, and algebra. Underlying this connection is the realization that unit groups profoundly shape the structure of any containing monoids. For example, the endomorphism monoid of a mathematical object is restricted by its isomorphism group. Conversely, important properties of monoids of transformations can often be translated into properties of permutation groups and lead to natural questions about group actions on partitions and sections. In this seminar, we will look at several cases of transversal properties. This is joint work with João Araújo (Universidade Nova de Lisboa), João Pedro Araújo (Stanford University), Peter J. Cameron (University of St Andrews), and Pablo Spiga (University of Milano-Bicocca).
Monday, 25 November, from 14:00 to 15:00.