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SINGREP SIGNED

Linking singularity theory and representation theory with homological methods

Total Cost €

0

EC-Contrib. €

0

Partnership

0

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 SINGREP project word cloud

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

university    eleonore    geometric    marsh    singular    integral    differential    varieties    operators    representation    normal    positive    theoretic    speaking    cohen    passes    categories    considerations    point    commutative    modules    breakdown    phenomena    relation    cluster    rings    theoretical    reflection    robot    leeds    pseudo    supervised    techniques    points    complete    homological    correspondence    construction    groups    geometry    directions    understand    singularity    integrate    maximal    lies    distant    nc    macaulay    analytical    quivers    theory    indeterminacy    leader    faber    practical    exploited    algebra    corresponds    necessarily    discriminants    bridge    polynomial    geometrically    intersection    singularities    crossing    resolutions    robert    algebraic    friezes    zerosets    seemingly    cusps    characterization    rs    dimension    group    break    serve    tries    arm    constructed    apart    global    ring    equations    situation    noncommutative    crepant    scientific    collapse    roughly    mckay    computation   

Project "SINGREP" data sheet

The following table provides information about the project.

Coordinator
UNIVERSITY OF LEEDS 

Organization address
address: WOODHOUSE LANE
city: LEEDS
postcode: LS2 9JT
website: www.leeds.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]
 Total cost 183˙454 €
 EC max contribution 183˙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-2017
 Funding Scheme MSCA-IF-EF-ST
 Starting year 2018
 Duration (year-month-day) from 2018-08-01   to  2020-07-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITY OF LEEDS UK (LEEDS) coordinator 183˙454.00

Map

 Project objective

In algebraic geometry one tries to understand and explain geometric phenomena of zerosets of polynomial equations (algebraic varieties) with algebraic techniques. Singularities of algebraic varieties are, roughly speaking, points of indeterminacy, where most analytical methods collapse. Geometrically, this corresponds e.g. to cusps or crossing points. In a practical example, the arm of a robot can break if it passes through a singular point, which could result in a complete breakdown of the system. Such a situation should be avoided by theoretical considerations.

This project lies at the intersection of singularity theory, (non-commutative) algebraic geometry, commutative algebra, and representation theory. The main goal is to develop homological methods to understand geometric phenomena of algebraic varieties in the presence of singularities and use them to study representation theoretic concepts such as cluster categories and friezes. The project will provide a bridge between these seemingly distant areas that can be exploited in both directions.

The specific research objectives: (1) Construction of noncommutative (crepant) resolutions of singularities (NC(C)Rs), in particular for not necessarily normal varieties/rings: computation of global dimension, application to positive characteristic (global dimension of ring of differential operators) (2) McKay correspondence for reflection groups: study of the geometry of discriminants of pseudo-reflection groups and their relation to the representation theory of the groups, characterization of McKay quivers (3) Friezes and singularities: show how (higher) integral friezes can be constructed from cluster categories and categories of maximal Cohen-Macaulay modules

The project will be carried out by Eleonore Faber, supervised by Robert Marsh at the University of Leeds. Apart from the scientific value, this project should serve to integrate Faber in the algebra research group and to establish her as a research leader.

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

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