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HyperK SIGNED

Modern Aspects of Geometry: Categories, Cycles and Cohomology of Hyperkähler Varieties

Total Cost €

0

EC-Contrib. €

0

Partnership

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 HyperK project word cloud

Explore the words cloud of the HyperK project. It provides you a very rough idea of what is the project "HyperK" about.

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Project "HyperK" data sheet

The following table provides information about the project.

Coordinator
RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAT BONN 

Organization address
address: REGINA PACIS WEG 3
city: BONN
postcode: 53113
website: www.uni-bonn.de

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Germany [DE]
 Total cost 8˙529˙641 €
 EC max contribution 8˙529˙641 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2019-SyG
 Funding Scheme ERC-SyG
 Starting year 2020
 Duration (year-month-day) from 2020-09-01   to  2026-08-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    RHEINISCHE FRIEDRICH-WILHELMS-UNIVERSITAT BONN DE (BONN) coordinator 3˙931˙798.00
2    UNIVERSITE DE PARIS FR (PARIS) participant 1˙781˙750.00
3    UNIVERSITE PARIS-SACLAY FR (SAINT AUBIN) participant 1˙764˙593.00
4    COLLEGE DE FRANCE FR (PARIS) participant 1˙051˙500.00
5    UNIVERSITE PARIS DIDEROT - PARIS 7 FR (PARIS) participant 0.00
6    UNIVERSITE PARIS-SUD FR (ORSAY CEDEX) participant 0.00

Map

 Project objective

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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