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CatDT

Financiado

Categorified Donaldson Thomas Theory

According to string theory, coherent sheaves on three-dimensional Calabi-Yau spaces encode fundamental properties of the universe. On the other hand, they have a purely mathematical definition. We will develop and use the new fiel... ver más

30/04/2023

UEDIN

1M€

Presupuesto del proyecto: 1M€

Líder del proyecto

THE UNIVERSITY OF EDINBURGH No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Ver 3 Participantes

Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2023-04-30

Línea de financiación objetivo El proyecto se financió a través de la siguiente ayuda:

ERC-2017-STG: ERC Starting Grant

I+D

Cerrada hace 8 años

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3 Participantes

UEDIN

1.22M€ | Lider

SALJOAR, S.A.

658.26K€ | Participante

UNIVERSITY OF GLASGOW

17.66K€ | Participante

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Últimas noticias

25-11-2024: ECE En las últimas 48 horas el Organismo ECE ha otorgado 52 concesiones

25-11-2024: CMVAMADRID En las últimas 48 horas el Organismo CMVAMADRID ha otorgado 1 concesiones

25-11-2024: FUNDACION-EOI En las últimas 48 horas el Organismo FUNDACION EOI ha otorgado 6 concesiones

Duración del proyecto: 66 meses Fecha Inicio: 2017-10-27
Fecha Fin: 2023-04-30

Líder del proyecto

THE UNIVERSITY OF EDINBURGH

TRL 4-5

Presupuesto del proyecto 1M€

Descripción del proyecto According to string theory, coherent sheaves on three-dimensional Calabi-Yau spaces encode fundamental properties of the universe. On the other hand, they have a purely mathematical definition. We will develop and use the new field of categorified Donaldson-Thomas (DT) theory, which counts these objects. Via the powerful perspective of noncommutative algebraic geometry, this theory has found application in recent years in a wide variety of contexts, far from classical algebraic geometry. Categorification has proved tremendously powerful across mathematics, for example the entire subject of algebraic topology was started by the categorification of Betti numbers. The categorification of DT theory leads to the replacement of the numbers of DT theory by vector spaces, of which these numbers are the dimensions. In the area of categorified DT theory we have been able to prove fundamental conjectures upgrading the famous wall crossing formula and integrality conjecture in noncommutative algebraic geometry. The first three projects involve applications of the resulting new subject: 1. Complete the categorification of quantum cluster algebras, proving the strong positivity conjecture. 2. Use cohomological DT theory to prove the outstanding conjectures in the nonabelian Hodge theory of Riemann surfaces, and the subject of Higgs bundles. 3. Prove the comparison conjecture, realising the study of Yangian quantum groups and the geometric representation theory around them as a special case of DT theory. The final objective involves coming full circle, and applying our recent advances in noncommutative DT theory to the original theory that united string theory with algebraic geometry: 4. Develop a generalised theory of categorified DT theory extending our results in noncommutative DT theory, proving the integrality conjecture for categories of coherent sheaves on Calabi-Yau 3-folds.

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