ChromSpaces
Financiado
Chromatic homotopy theory of spaces
Many current developments in stable homotopy theory are guided by the ‘chromatic perspective’. One decomposes a spectrum into its monochromatic pieces, each of which is a localization corresponding to one of the prime fields of hi...
Many current developments in stable homotopy theory are guided by the ‘chromatic perspective’. One decomposes a spectrum into its monochromatic pieces, each of which is a localization corresponding to one of the prime fields of higher algebra (the Morava K-theories, generalizing the prime fields Q and F_p of ordinary algebra). The goal of this proposal is to study the chromatic decomposition of spaces, as opposed to that of spectra. I will establish structural results for the category of all monochromatic spaces ‘of a given color’ and study the assembly question: how to put the pieces back together to retrieve information about the original space? The techniques are informed by my recent results relating monochromatic spaces to spectral Lie algebras, which generalize Quillen’s rational homotopy theory to all the other relevant chromatic localizations of homotopy theory. More precisely, this research has the following goals. 1. Develop the structure theory of spectral Lie algebras and apply it to monochromatic spaces. This includes understanding Koszul duality between spectral Lie algebras and commutative ring spectra, with applications to a conjecture of Francis-Gaitsgory, and decomposition results for spectral Lie algebras, with applications to torsion exponents of homotopy groups, building on classical work of Cohen-Moore-Neisendorfer. 2. Develop a theory of transchromatic spectral Lie algebras, explaining how the different monochromatic pieces of homotopy theory interact. This connects to my previous work on the Goodwillie tower of homotopy theory and Tate coalgebras.
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Duración del proyecto: 64 meses
Fecha Inicio: 2020-08-17
Fecha Fin: 2025-12-31
Fecha Fin: 2025-12-31
Línea de financiación: concedida
El organismo H2020 notifico la concesión del proyecto el día 2020-08-17
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
ERC-2020-STG:
ERC STARTING GRANTS
Cerrada
hace 5 años
Presupuesto
El presupuesto total del proyecto asciende a
2M€
Líder del proyecto
UNIVERSITEIT UTRECHT
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
Perfil tecnológico
TRL
4-5
240.06K€ |
Participante