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HPD-inv of TBR

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Homological Projective Duality invariance of the Tate Beilinson and Riemann c...

Homological Projective Duality invariance of the Tate Beilinson and Riemann conjectures This project will be carried out at the Warwick Mathematics Institute under the supervision of Prof. John Greenlees; I have worked for the past eight years at MIT and I will move in 2020 to the University of Warwick as an Associat... ver más

31/08/2022

UNIVERSITY OF WARW...

225K€

Presupuesto del proyecto: 225K€

Líder del proyecto

UNIVERSITY OF WARWICK 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 2022-08-31

MSCA-IF-2019: Individual Fellowships

I+D

Cerrada hace 5 años

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1 Participantes

UNIVERSITY OF WARWICK

224.93K€ | Lider

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Duración del proyecto: 28 meses Fecha Inicio: 2020-04-17
Fecha Fin: 2022-08-31

Líder del proyecto

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

TRL 4-5

Presupuesto del proyecto 225K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto This project will be carried out at the Warwick Mathematics Institute under the supervision of Prof. John Greenlees; I have worked for the past eight years at MIT and I will move in 2020 to the University of Warwick as an Associate Professor. Three of the most important conjectures in mathematics - the Tate conjecture, the Beilinson conjecture and the generalized Riemann hypothesis - concern the location and order of the zeros/poles of the L-functions associated to algebraic varieties. For example, in the particular case of an elliptic curve, the Beilinson conjecture reduces to the Birch and Swinnerton-Dyer conjecture, and in the particular case of a point, the generalized Riemann hypothesis reduces to the Riemann hypothesis. These are two of the seven Millenium Prize Problems. The first objective of this project is to prove that the conjectures of Tate, Beilinson, and Riemann, are invariant under homological projective duality in the sense of Kuznetsov. The second objective is to combine this invariance result with the different homological projective dualities in the literature in order to obtain not only a proof of the conjectures of Tate and Beilinson in numerous new cases but also an equivalence between the generalized Riemann hypothesis of very different algebraic varieties. These objectives will greatly improve the state-of-the-art of the Tate and Beilinson conjectures and will considerably deepen our understanding of the generalized Riemann hypothesis. In order to achieve them, I will combine Kontsevich's noncommutative viewpoint on algebraic geometry with mathematical tools from several different areas (e.g., algebraic topology, derived categories, algebraic K-theory, etc). This will enhance my creative and innovative potential, will foster my professional maturity and independence, will diversify my technical skills, and also will enable me to receive advanced training. Hence, this project is directly aligned with the MSCA-IF-EF-RI objectives.

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