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SINGREP

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Linking singularity theory and representation theory with homological methods

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... ver más

31/07/2020

UNIVLEEDS

183K€

Presupuesto del proyecto: 183K€

Líder del proyecto

UNIVERSITY OF LEEDS No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2020-07-31

MSCA-IF-2017: Individual Fellowships

I+D

Cerrada hace 7 años

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1 Participantes

UNIVLEEDS

183.45K€ | Lider

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Duración del proyecto: 28 meses Fecha Inicio: 2018-03-09
Fecha Fin: 2020-07-31

Líder del proyecto

UNIVERSITY OF LEEDS No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 183K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto 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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