Giovedì 5 Dicembre 2024 alle ore 14:00, nel quadro del ciclo di seminari Al@Bicocca, Lorenzo Guerra (Università degli Studi di Milano-Bicocca) parlerà di
Titolo: The cohomology of the symmetric groups, Hopf rings and extended symmetric powers
Abstract: The direct sum of the cohomology groups H∗(Σn; V⊗n) of the symmetric group Σn on n objects, with coefficients in the representation given by the nth tensor power of a graded algebra V, is endowed with a very rich algebraic structure. Precisely, it is a Hopf ring, a ring object in the category of cocommutative coalgebras. In my talk, I will recall the definition of Hopf ring, and I will show the aforementioned structure can be used to effectively perform computations in the cohomology rings above. I will then discuss the relation with the cohomology of the extended symmetric powers of topological spaces, which are widely used by topologists. This is mostly based on an article published in 2023 by myself, Paolo Salvatore, and Dev Sinha. Finally, I will briefly discuss applications of this framework (some of them more recent): an algebraic one to finite reflection groups, and a topological and representation theoretic one to unordered flag manifolds.
Informazioni per partecipare
Il seminario si terrà in Aula 3014 (3° Piano) - Edificio U5, Università degli Studi di Milano-Bicocca e sarà disponibile anche online al seguente link Webex