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STABRT

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Cerrado

Stability conditions in Representation Theory and beyond

The overall aim of this project is to establish a new connection between representation theory and algebraic geometry. In recent years, great progress has been done in the understanding of stability conditions over module categori... ver más

30/09/2023

UPCité

185K€

Presupuesto del proyecto: 185K€

Líder del proyecto

UNIVERSITE PARIS CITE 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 2023-09-30

MSCA-IF-2019: Individual Fellowships

I+D

Cerrada hace 5 años

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1 Participantes

UPCité

184.71K€ | Lider

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Duración del proyecto: 41 meses Fecha Inicio: 2020-04-20
Fecha Fin: 2023-09-30

Líder del proyecto

UNIVERSITE PARIS CITE No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 185K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto The overall aim of this project is to establish a new connection between representation theory and algebraic geometry. In recent years, great progress has been done in the understanding of stability conditions over module categories, notably in the description of the wall and chamber structure of finite-dimensional algebras via tau-tilting theory. During this fellowship I will undertake research that will lead to a deeper understanding of these stability conditions and I will apply these tools to the Homological Mirror Symmetry Program and the study of toric varieties. It is known that most of the information of wall-crossing phenomena of cluster algebras is encoded in the so-called cluster scattering diagram, recently introduced by Gross-Hacking-Keel-Kontsevich. In a seminal paper, Bridgeland showed that these scattering diagrams are intimately related with the wall and chamber structure of certain jacobian algebras. The wall and chamber structure of an algebra has a rich combinatorial structure. In particular, it has the structure of what is known as a fan in toric geometry. Each fan determines uniquely a toric variety. In this project, I will study tau-tilting theory and stability conditions in four different ways. From the more representation theoretic to the more geometric, these are the following: I will attack problems on tau-tilting theory related with the finitistic dimension conjecture; I will show how the wall and chamber structure of two algebras encode the homological relation between them; I will use the knowledge about wall and chamber structures for finite-dimensional algebra to study wall-crossing phenomena beyond the realm of cluster algebras; I will establish the relation between certain homological properties of finite-dimensional algebras with the homological properties of their associated toric varieties.

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