Hola,
¿eres nuevo aquí?

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

Tengo cuenta

Regístrate

Ver video

PosLieRep

Financiado

Cerrado

Positivity in Lie groups and representation varieties

Lie groups lie at the heart of mathematics. They play an important role in geometry, analysis, number theory, algebraic geometry and representation theory. As they describe symmetries of a space or a system they also appear promin... ver más

30/09/2026

MPG

2M€

Presupuesto del proyecto: 2M€

Líder del proyecto

MAXPLANCKGESELLSCHAFT ZUR FORDERUNG DER WISSE... 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 3 Participantes

Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2021-05-22

ERC-2020-ADG: ERC ADVANCED GRANT

I+D

Cerrada hace 4 años

0% 100% 100%

Información adicional privada

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

3 Participantes

MPG

1.82M€ | Lider

EQUIPOS NUCLEARES SA SME

614.88K€ | Participante

UHEI

207.94K€ | 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

Proyectos interesantes

GELATI Geometry of exceptional Lie algebras à la Tits 222K€ Cerrado

DiGGeS Discrete Groups and Geometric Structures 1M€ Cerrado

CORELG Computation with real Lie Groups 181K€ Cerrado

RESFINGROUP Invariants of residually finite groups graphs groups and d... 155K€ Cerrado

MTM2014-59456-P ESPACIOS SINGULARES, CATEGORIAS DERIVADAS Y TEORIAS BIVARIAN... 29K€ Cerrado

COMBGEOREP Combinatorial and geometric methods in representation theory 213K€ Cerrado

Duración del proyecto: 64 meses Fecha Inicio: 2021-05-22
Fecha Fin: 2026-09-30

Líder del proyecto

MAXPLANCKGESELLSCHAFT ZUR FORDERUNG DER WISSE... No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 2M€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto Lie groups lie at the heart of mathematics. They play an important role in geometry, analysis, number theory, algebraic geometry and representation theory. As they describe symmetries of a space or a system they also appear prominently in theoretical physics. Not every system realizes the full amount of symmetry, it is therefore of key importance to investigate not only Lie groups, but also their subgroups, and in particular their discrete subgroups, which are often linked to geometric or arithmetic structures. This projects builds upon new developments in the theory of Lie groups, in particular the intro- duction of total positivity in split real Lie groups on the one hand and new exiciting phenomena in the study of discrete subgroups, in particular the emergence of higher Teichmüller spaces. Higher Teichmüller spaces generalize the classical theory of Fricke-Teichmüller space in the context of simple Lie groups of higher rank. The existence of higher Teichmu ̈ller spaces came as a surprise, and their discovery and investigation led to various other interesting developments, including an exciting interplay with the theory of Higgs bundles as well as with supersymmetric field theories in theoretical physics. In this proposal we develop a unifying framework for higher Teichmüller spaces, which comprises the two known families, Hitchin components and maximal representations, but conjecturally also two new families. The basis for this conjectural unified theory lies in a new notion of positivity in Lie groups, which generalizes Lusztig’s total positivity in the context of arbitrary real Lie groups that are not necessarily split. This generalization of total positivity is of interest in its own right and leads to many exciting questions and conjectures that will be addressed in this proposal. The three main themes of the proposed project are Positivity in Lie groups, Positive representations as higher Teichmüller spaces, and Symplectic geometry of representati

Conecta tu I+D

Entra hoy

¿Olvidé mi contraseña?

Financiación

Empresas

CTIs/Universidades

Proyectos

Investigadores