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StabilityDTCluster SIGNED

Stability conditions, Donaldson-Thomas invariants and cluster varieties

Total Cost €

0

EC-Contrib. €

0

Partnership

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 StabilityDTCluster project word cloud

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

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Project "StabilityDTCluster" data sheet

The following table provides information about the project.

Coordinator
THE UNIVERSITY OF SHEFFIELD 

Organization address
address: FIRTH COURT WESTERN BANK
city: SHEFFIELD
postcode: S10 2TN
website: www.shef.ac.uk

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
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 Coordinator Country United Kingdom [UK]
 Total cost 1˙556˙550 €
 EC max contribution 1˙556˙550 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-ADG
 Funding Scheme ERC-ADG
 Starting year 2015
 Duration (year-month-day) from 2015-10-01   to  2020-09-30

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    THE UNIVERSITY OF SHEFFIELD UK (SHEFFIELD) coordinator 1˙556˙550.00

Map

 Project objective

This proposal is concerned with the homological properties of Calabi-Yau threefolds, the geometric structures which play a crucial role in string theory. Rather than working directly with categories of sheaves, we focus on a closely-related class of models defined using quivers with potentials, which have themselves been the subject of intensive research over the last decade.

Associated to a quiver with potential are two complex manifolds: the space of stability conditions and the cluster variety. Recent work by physicists Gaiotto, Moore and Neitzke suggests that there is a remarkable geometric relationship between these spaces, involving Donaldson-Thomas invariants and the Kontsevich-Soibelman wall-crossing formula. Work by the PI and others over the last couple of years has paved the way for a rigorous mathematical understanding of this relationship. This has the potential to open up new vistas in algebra and geometry, as well as greatly enhancing our understanding of the mathematics of quantum field theory.

Our proposal combines powerful general constructions with specific computable examples. We will work initially with a class of examples related to triangulated surfaces; here the relevant spaces can be identified with familiar objects in the topology of surfaces, including moduli spaces of quadratic differentials, projective structures and local systems. These examples already involve deep mathematics, and are closely related to quantum field theories of current interest in theoretical physics.

This proposal involves an unusually wide range of mathematics. Our ambition is to assemble a team of 4 research assistants having a sufficiently broad expertise to make progress on this exciting multi-disciplinary project. The PI is in a perfect position to lead such a team: he invented stability conditions, carried out important work on Donaldson-Thomas invariants, and proved a major theorem which forms one of the starting points of the proposal.

 Publications

year authors and title journal last update
List of publications.
2018 Dylan G.L. Allegretti and Tom Bridgeland
The monodromy of meromorphic projective structures
published pages: , ISSN: , DOI:
2019-07-05
2017 Dylan G.L. Allegretti
Stability conditions and cluster varieties from quivers of type A
published pages: , ISSN: , DOI:
2019-07-05
2017 Tom Bridgeland
Riemann-Hilbert problems for the resolved conifold
published pages: , ISSN: , DOI:
2019-07-05
2018 Dylan G.L. Allegretti
Virus symbols as cluster co-ordinates
published pages: , ISSN: , DOI:
2019-07-05
2018 Anna Barbieri
A Riemann-Hilbert problem for uncoupled BPS structures
published pages: , ISSN: , DOI:
2019-07-05
2017 Tom Bridgeland
Riemann-Hilbert problems from Donaldson-Thomas theory
published pages: , ISSN: , DOI:
2019-07-05

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