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HyperK

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Modern Aspects of Geometry Categories Cycles and Cohomology of Hyperka hler Va...

Modern Aspects of Geometry Categories Cycles and Cohomology of Hyperka hler Varieties The space around us is curved. Ever since Einstein’s discovery that gravity bends space and time, mathematicians and physicists have been intrigued by the geometry of curvature. Among all geometries, the hyperkähler world exhibit... ver más

31/08/2026

RHEINISCHE FRIEDRI...

9M€

Presupuesto del proyecto: 9M€

Líder del proyecto

RHEINISCHE FRIEDRICHWILHELMSUNIVERSITAT BONN No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

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Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2019-12-04

ERC-2019-SyG: ERC Synergy Grant

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Cerrada hace 6 años

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6 Participantes

RHEINISCHE FRIEDRICHWILHELMS...

3.93M€ | Lider

MENADIONA

320.56K€ | Participante

COLLEGE DE FRANCE

N.D. | Participante

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Duración del proyecto: 80 meses Fecha Inicio: 2019-12-04
Fecha Fin: 2026-08-31

Líder del proyecto

RHEINISCHE FRIEDRICHWILHELMSUNIVERSITAT BONN No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 9M€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto The space around us is curved. Ever since Einstein’s discovery that gravity bends space and time, mathematicians and physicists have been intrigued by the geometry of curvature. Among all geometries, the hyperkähler world exhibits some of the most fascinating phenomena. The special form of their curvature makes these spaces beautifully (super-)symmetric and the interplay of algebraic and transcendental aspects secures them a special place in modern mathematics. Algebraic geometry, the study of solutions of algebraic equations, is the area of mathematics that can unlock the secrets in this realm of geometry and that can describe its central features with great precision. HyperK combines background and expertise in different branches of mathematics to gain a deep understanding of hyperkähler geometry. A number of central conjectures that have shaped algebraic geometry as a branch of modern mathematics since Grothendieck’s fundamental work shall be tested for this particularly rich geometry. The expertise covered by the four PIs ranges from category theory over the theory of algebraic cycles to cohomology of varieties. Any profound advance in hyperkähler geometry requires a combination of all three approaches. The concerted effort of the PIs, their collaborators, and their students will lead to major progress in this area. The goal of HyperK is to advance hyperkähler geometry to a level that matches the well established theory of K3 surfaces, the two-dimensional case of hyperkähler geometry. We aim at proving fundamental results concerning cycles, at classifying Hodge structures and cohomological invariants, and at unifying geometry and derived categories. Specific topics in- clude the splitting conjecture, the Hodge conjecture in small degrees, moduli spaces in derived categories, geometric K3 categories, and special subvarieties. The ultimate goal of HyperK is to draw a clear and distinctive picture of the hyperkähler landscape as a central part of mathematic

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