Hola,
¿eres nuevo aquí?

Regístrate gratis y conecta tu empresa con financiación pública, partners y proyectos.

Tengo cuenta

Regístrate

Ver video

StabCondEn

Financiado

Cerrado

Stability Conditions Moduli Spaces and Enhancements

I will introduce new techniques to address two big open questions in the theory of derived/triangulated categories and their many applications in algebraic geometry. The first one concerns the theory of Bridgeland stability condi... ver más

31/01/2024

UMIL

786K€

Presupuesto del proyecto: 786K€

Líder del proyecto

UNIVERSITA DEGLI STUDI DI MILANO No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Ver 2 Participantes

Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2024-01-31

ERC-2017-COG: ERC Consolidator Grant Scope:Objectives

I+D

Cerrada hace 8 años

0% 100% 100%

Características del participante

Este proyecto no cuenta con búsquedas de partenariado abiertas en este momento.

Información adicional privada

No hay información privada compartida para este proyecto. Habla con el coordinador.

2 Participantes

UMIL

785.87K€ | Lider

Natra Oñati, S.A.

1.72M€ | Participante

Conecta tu I+D

¿Tienes un proyecto y buscas un partner? Gracias a nuestro motor inteligente podemos recomendarte los mejores socios y ponerte en contacto con ellos. Te lo explicamos en este video

Duración del proyecto: 72 meses Fecha Inicio: 2018-01-22
Fecha Fin: 2024-01-31

Líder del proyecto

UNIVERSITA DEGLI STUDI DI MILANO No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 786K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto I will introduce new techniques to address two big open questions in the theory of derived/triangulated categories and their many applications in algebraic geometry. The first one concerns the theory of Bridgeland stability conditions, which provides a notion of stability for complexes in the derived category. The problem of showing that the space parametrizing stability conditions is non-empty is one of the most difficult and challenging ones. Once we know that such stability conditions exist, it remains to prove that the corresponding moduli spaces of stable objects have an interesting geometry (e.g. they are projective varieties). This is a deep and intricate problem. On the more foundational side, the most successful approach to avoid the many problematic aspects of the theory of triangulated categories consisted in considering higher categorical enhancements of triangulated categories. On the one side, a big open question concerns the uniqueness and canonicity of these enhancements. On the other side, this approach does not give a solution to the problem of describing all exact functors, leaving this as a completely open question. We need a completely new and comprehensive approach to these fundamental questions. I intend to address these two sets of problems in the following innovative long-term projects: 1. Develop a theory of stability conditions for semiorthogonal decompositions and its applications to moduli problems. The main applications concern cubic fourfolds, Calabi-Yau threefolds and Calabi-Yau categories. 2. Apply these new results to the study of moduli spaces of rational normal curves on cubic fourfolds and their deep relations to hyperkaehler geometry. 3. Investigate the uniqueness of dg enhancements for the category of perfect complexes and, most prominently, of admissible subcategories of derived categories. 4. Develop a new theory for an effective description of exact functors in order to prove some related conjectures.

Conecta tu I+D

Entra hoy

Forgot your password?

Financiación

Empresas

CTIs/Universidades

Proyectos

Investigadores