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AGAGAP SIGNED

Algebraic Group Actions in Geometry, Arithmetic, and Physics

Total Cost €

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EC-Contrib. €

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Partnership

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Project "AGAGAP" data sheet

The following table provides information about the project.

Coordinator
THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD 

Organization address
address: WELLINGTON SQUARE UNIVERSITY OFFICES
city: OXFORD
postcode: OX1 2JD
website: www.ox.ac.uk

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 United Kingdom [UK]
 Project website http://www.maths.ox.ac.uk/people/frances.kirwan
 Total cost 195˙454 €
 EC max contribution 195˙454 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2016
 Funding Scheme MSCA-IF-EF-ST
 Starting year 2017
 Duration (year-month-day) from 2017-08-17   to  2019-08-16

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD UK (OXFORD) coordinator 195˙454.00

Map

 Project objective

'Geometry, arithmetic, and quantum physics historically have had many points of intersection. This project will use recent techniques in algebraic group actions, especially those of Kirwan, to address problems of overlapping interest to distinct research groups at the University of Oxford – Algebraic Geometry, Number Theory, Mathematical Physics, and the Centre for Quantum Mathematics and Computation.

Consider the following long-standing, a priori unrelated, questions. What is the minimal degree curve that passes through n points in general position in the plane (Nagata conjecture)? What is the growth rate of the number of integer lattice points in a variety (for us, universal torsor over a Fano variety) with respect to a height function (Manin conjecture)? How can one work with quantum entanglements of different qualitative character and associated entropies in a rigorous yet experimentally friendly way?

These open questions turn out to admit a common source, at least in a large class of problems of interest. The crucial ingredient is a suitable 'homotopic replacement for a universal torsor' -- arising, in nice cases, from a key difference with topology, since in algebraic geometry algebraic affine line bundles needn't be vector bundles -- that often allows one to reduce to studying a simpler problem in group actions attached to an affine space rather than to a complicated variety or even more complicated universal torsor.'

 Publications

year authors and title journal last update
List of publications.
2018 Gergely Bérczi, Brent Doran, Thomas Hawes, Frances Kirwan
Geometric invariant theory for graded unipotent groups and applications
published pages: 826-855, ISSN: 1753-8416, DOI: 10.1112/topo.12075
Journal of Topology 11/3 2020-04-14
2019 Seunghwoi Han, Lisa Ortmann, Hyunwoong Kim, Yong Woo Kim, Takashi Oka, Alexis Chacon, Brent Doran, Marcelo Ciappina, Maciej Lewenstein, Seung-Woo Kim, Seungchul Kim, Alexandra S. Landsman
Extraction of higher-order nonlinear electronic response in solids using high harmonic generation
published pages: , ISSN: 2041-1723, DOI: 10.1038/s41467-019-11096-x
Nature Communications 10/1 2020-04-14

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The information about "AGAGAP" are provided by the European Opendata Portal: CORDIS opendata.

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