CAPCAM
Financiado
Cut-and-paste conjectures and multicurves
Knot theory has seen extraordinary developments over the past decades. The arrival of modern homological knot invariants has had far-reaching implications beyond low-dimensional topology, giving insight into old problems through...
Knot theory has seen extraordinary developments over the past decades. The arrival of modern homological knot invariants has had far-reaching implications beyond low-dimensional topology, giving insight into old problems through deep ties between knot theory, algebraic geometry, representation theory, Floer theory, and physics.My ERC project aims to establish a new perspective on knot homology theories using a new type of invariants, so-called multicurves. As objects of Fukaya categories of simple surfaces, these multicurve invariants make local versions of knot homology theories amenable to essentially combinatorial techniques. Thanks to their exceptional geometric and gluing properties, multicurves are ideally suited to implement the divide-and-conquer principle for attacking hard open problems. In fact, I have not only been directly involved in the definition of three of these invariants, but I have also applied them to resolve several open conjectures in the field already.The purpose of my research programme is to investigate fundamental open problems in low-dimensional topology that require a deeper understanding of the new technology of multicurves. To this end, I will pursue the following four lines of basic research: I will investigate the topological properties of the new invariants and their relation to classical invariants. I will explore the existence of local versions of various spectral sequences that are known to relate knot homology theories. I will make the invariants more computable. Finally, I will apply the generic principles that underlie the definition of multicurves to other settings.
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Duración del proyecto: 59 meses
Fecha Inicio: 2024-04-01
Fecha Fin: 2029-03-31
Fecha Fin: 2029-03-31
Línea de financiación: concedida
El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2024-04-01
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
ERC-2023-STG:
ERC STARTING GRANTS
Cerrada
hace 2 años
Presupuesto
El presupuesto total del proyecto asciende a
1M€
Líder del proyecto
RUHRUNIVERSITAET BOCHUM
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
Perfil tecnológico
TRL
4-5