ABCD
Financiado
Around Braids, Categories and Distances
This proposal aims at addressing classical problems about the braid group by making use of recent advances in higher representation theory. More precisely, I want to use Khovanov-Seidel categorified Burau representation and Bappat...
This proposal aims at addressing classical problems about the braid group by making use of recent advances in higher representation theory. More precisely, I want to use Khovanov-Seidel categorified Burau representation and Bappat-Deopurkar-Licata's work on stability conditions to work on the faithfulness problem for the Burau representation and on the Haagerup question for the braid group.
The faithfulness of the Burau representation for the 4-strand braid group is one the oldest and most tantalizing problems in braid group theory. I strongly hope that new light can be shed on it by using recent tools from higher representation theory. My strategy is to develop with Licata a ping-pong argument, which will rely on a diagrammatic description of morphisms in the category of bimodules over the zig-zag algebra. Then a fine control of the decategorification process will be needed, that I will study with Bonnafé.
Braid groups also play a major role in geometric group theory, a field of research that arose under the impulse of Gromov. Amongst open questions, knowing whether the braid groups enjoy the Haagerup property is a central one, as it has ties with several open conjectures. I plan to use Bappat-Deopurkar-Licata's work on Bridgeland stability conditions on the category of representations of the zig-zag algebra to build a space with walls on which the braid groups in type A would act. This would yield a proof of the Haagerup property for braid groups in type A.
Both of these work problems are major challenges in braid theory, and my approach to study them will create innovative mathematics entangling tools from several fields (geometric group theory, triangulated categories, diagrammatic algebra). This project will only be made possible thanks to the help of world-leading experts in Canberra and Montpellier, who will assist me in using mathematical tools I am not always familiar with.
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Duración del proyecto: 24 meses
Fecha Inicio: 2022-08-01
Fecha Fin: 2024-08-31
Fecha Fin: 2024-08-31
Línea de financiación: concedida
El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2024-08-31
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
HORIZON-MSCA-2021-PF-01-01:
MSCA Postdoctoral Fellowships 2021
Cerrada
hace 3 años
Presupuesto
El presupuesto total del proyecto asciende a
136K€
Líder del proyecto
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE...
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
Perfil tecnológico
TRL
4-5
N.D. |
Participante