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ExplicitDarmonProg

Explicit Methods for the Darmon Programme

Total Cost €

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EC-Contrib. €

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Partnership

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 ExplicitDarmonProg project word cloud

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Project "ExplicitDarmonProg" data sheet

The following table provides information about the project.

Coordinator
THE UNIVERSITY OF WARWICK 

Organization address
address: Kirby Corner Road - University House
city: COVENTRY
postcode: CV4 8UW
website: www.warwick.ac.uk

contact info
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 Coordinator Country United Kingdom [UK]
 Project website http://homepages.warwick.ac.uk/
 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-2014
 Funding Scheme MSCA-IF-EF-ST
 Starting year 2015
 Duration (year-month-day) from 2015-09-01   to  2017-09-30

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    THE UNIVERSITY OF WARWICK UK (COVENTRY) coordinator 195˙454.00

Map

 Project objective

Elliptic curves are the heart of contemporary research in number theory. For example, their modularity played a crucial role in Wiles' proof of Fermat's Last Theorem. Understanding their rational points is the subject of the Birch and Swinnerton-Dyer Conjecture (BSD), one of the seven $1M Clay Mathematics Institute Millennium Prizes. This proposal is concerned with rational points on elliptic curves and linked to both BSD and modularity.

The Darmon Programme is an ambitious project initiated by Henri Darmon, aiming to provide constructions of points on elliptic curves over number fields, and to prove new cases of BSD. The proposed action is an initiative to extend the Darmon Programme, make known constructions explicit and algorithmic to provide extensive data that will be invaluable to researchers in the field, and guide further theoretical work.

Warwick has one of the largest and most active explicit number theory groups in the world, consisting of 2 professors, 3 lecturers, 8 research fellows and 12 PhD students, making it a natural host for the project. The supervisor Siksek, is a leading expert on elliptic curves, rational points and modularity, with considerable experience in supervising research including 5 Marie Curie fellows.

Masdeu did his undergraduate studies in Barcelona. He completed his PhD (McGill) under the supervision of Darmon, and therefore has intimate understanding of the Darmon Programme. Masdeu then worked as Ritt Assistant Professor at Columbia University before joining Warwick as a postdoc in 2014. Therefore his research experience has almost entirely been confined to North America, even though his ambition is to establish himself as an independent researcher at a prestigious European university. Masdeu has substantial research results with 8 papers accepted in strong journals. This project will integrate him into the European research environment, and give him new skills and research directions to enable him to realize his goal.

 Publications

year authors and title journal last update
List of publications.
2016 Xavier Guitart, Marc Masdeu, Mehmet Haluk Şengün
Uniformization of modular elliptic curves via p-adic periods
published pages: 458-502, ISSN: 0021-8693, DOI: 10.1016/j.jalgebra.2015.06.021
Journal of Algebra 445 2019-07-23
2017 Daniel Kohen, Ariel Martin Pacetti, Marc Masdeu
On Heegner points for primes of additive reduction ramifying in the base field
published pages: 1, ISSN: 0002-9947, DOI: 10.1090/tran/6990
Transactions of the American Mathematical Society 2019-07-23

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