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Homotopy theory of spaces of homomorphisms

In this project we propose to study homotopy theoretic properties of spaces of commuting elements in compact Lie groups. These spaces play an essential role in mathematical physics and geometry, but only in the last decade a syste... ver más

31/08/2021

UCPH

207K€

Presupuesto del proyecto: 207K€

Líder del proyecto

KOBENHAVNS UNIVERSITET No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2021-08-31

MSCA-IF-2018: Individual Fellowships

I+D

Cerrada hace 6 años

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Información adicional privada

No hay información privada compartida para este proyecto. Habla con el coordinador.

1 Participantes

UCPH

207.31K€ | Lider

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Duración del proyecto: 28 meses Fecha Inicio: 2019-04-10
Fecha Fin: 2021-08-31

Líder del proyecto

KOBENHAVNS UNIVERSITET No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 207K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto In this project we propose to study homotopy theoretic properties of spaces of commuting elements in compact Lie groups. These spaces play an essential role in mathematical physics and geometry, but only in the last decade a systematic study by homotopy theoretic methods has been initiated. Important open questions in the field concern the homology as well as the (stable) homotopy type. In the first part of the project, we attempt to prove a conjectural stable splitting theorem, which would establish an intriguing relationship between spaces of commuting elements and commuting varieties in Lie algebras, an object of classical interest in algebraic geometry. In the second part, we propose to investigate the phenomenon of homology stability for spaces of commuting elements in the unitary and orthogonal groups. Building on recent work of the experienced researcher, an approach to calculate the stable homology is presented. This is expected to uncover a wealth of previously unknown homology groups of these interesting spaces. The research conducted to achieve the project goals, together with the training in teaching and management received during the fellowship, will have a major positive impact on the career development of the experienced researcher. On the research level, this impact is through the acquisition of knowledge in new research areas, in particular in homology stability and the homotopy theory of Lie group actions. The project will be carried out in an exceptionally active and successful scientific community at the University of Copenhagen, supervised by a world expert in the homotopy theory of Lie groups. Completion of the project will serve as a springboard to build new collaborations and to enter further advanced projects in a range of areas. It is thus a perfect preparation for a high-level research career in mathematics.

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