Obiettivo This is a project in commutative algebra of positive characteristic, which has also many connections with algebraic geometry.The main goal of this project is to study the relations between some classes of rings that arise in prime characteristic, F-singularities, and three specific notions. These are the symmetric signature, a new invariant defined by the Experienced Researcher in his Ph.D. thesis; the generalized Hilbert-Kunz function, a recent generalization of the classical Hilbert-Kunz function studied intensively in prime characteristic algebra; and the FFRT property, a positive characteristic version of the notion of finite representation type, important in representation theory. As a guideline for the future research, eight concrete problems are stated and will be investigated by the Experienced Researcher with the help of the Supervisor. The strategy to complete this task include the acquisition of new knowledge, which will be obtained, among other things, also through the organization of weekly seminars with the collaboration of the host institution. The arguments of this project, F-singularities in particular, are important topics in commutative algebra and algebraic geometry which are developing and growing fast in these years, especially in the USA and in Japan. As a further way to promote the development of these topics also in Europe, the Experienced Researcher and the Supervisor plan to organize a small workshop which will take place in the host institution at the end of the fellowship. Campo scientifico natural sciencesmathematicspure mathematicsalgebracommutative algebranatural sciencesmathematicspure mathematicstopologynatural sciencesphysical sciencesastronomyplanetary sciencesnatural satellitesnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Parole chiave Prime characteristic methods Frobenius homomorphism Hilbert-Kunz function Singularity Finite representation type Programma(i) H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility Argomento(i) MSCA-IF-2015-EF - Marie Skłodowska-Curie Individual Fellowships (IF-EF) Invito a presentare proposte H2020-MSCA-IF-2015 Vedi altri progetti per questo bando Meccanismo di finanziamento MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF) Coordinatore UNIVERSITAT DE BARCELONA Contribution nette de l'UE € 158 121,60 Indirizzo GRAN VIA DE LES CORTS CATALANES 585 08007 Barcelona Spagna Mostra sulla mappa Regione Este Cataluña Barcelona Tipo di attività Higher or Secondary Education Establishments Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Partecipazione a programmi di R&I dell'UE Opens in new window Rete di collaborazione HORIZON Opens in new window Costo totale € 158 121,60
