Obiettivo This research proposal is in mathematics, its content is part of algebraic topology and homotopy theory. It aims at deepening our understanding of the homotopy theory of cosimplicial unstable (co-)algebras over the Steenrod algebra and its relation to the homotopy theory of cosimplicial spaces. This is achieved by new methods developed recently by the ER (Dr. Biedermann) and coauthors and by methods from Goodwillie calculus. Specifically, there are three closely related parts/work packages: 1. Prove a general vanishing theorem of higher obstructions for realizing a map on homology as a map of spaces. The theorem is known to hold in rational homotopy and in the mod p Massey-Peterson case. 2. Find an algebraic description of the first obstruction living in Andre-Quillen cohomology (AQC) to the existence of a realization of unstable coalgebras. 3. Define natural operations on AQC of unstable coalgebras with general coefficients.As part of the risk management we describe two further fallback projects: 4. Study the Goodwillie tower of the identity functor of simplicial unstable algebras and relate its layers to AQC. 5. Describe the algebra of homotopy operations on simplicial commutative algebras for odd primes p. These projects are parts of a program of the ER to investigate realization problems and rigidity results associated to singular (co-)homology. A longterm goal (beyond the time frame of the fellowship) is to develop a deformation theory of unstable (co-)algebras over the Steenrod algebra and their realizing homotopy types in the mod p case. Campo scientifico natural sciencescomputer and information sciencessoftwarenatural sciencesmathematicspure mathematicsalgebracommutative algebranatural sciencescomputer and information sciencescomputational sciencenatural sciencesmathematicspure mathematicstopologyalgebraic topologysocial sciencessociologygovernancecrisis management 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-2014-EF - Marie Skłodowska-Curie Individual Fellowships (IF-EF) Invito a presentare proposte H2020-MSCA-IF-2014 Vedi altri progetti per questo bando Meccanismo di finanziamento MSCA-IF-EF-ST - Standard EF Coordinatore UNIVERSITE PARIS 13 Contribution nette de l'UE € 185 076,00 Indirizzo AVENUE JEAN-BAPTISTE CLEMENT 99 93430 Villetaneuse Francia Mostra sulla mappa Regione Ile-de-France Ile-de-France Seine-Saint-Denis 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 € 185 076,00
