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Groups operator algebras and dynamics

The proposed research project fits into the broad programme of studying C*-algebras and groups dynamical origin, and is highly interdisciplinary in nature; it advances novel interactions among operator algebras, group theory, and... ver más

30/04/2024

UNIVERSITY OF GLAS...

213K€

Presupuesto del proyecto: 213K€

Líder del proyecto

UNIVERSITY OF GLASGOW 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 2024-04-30

MSCA-IF-2020: Individual Fellowships

I+D

Cerrada hace 4 años

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Información adicional privada

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

1 Participantes

UNIVERSITY OF GLASGOW

212.93K€ | Lider

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Duración del proyecto: 37 meses Fecha Inicio: 2021-03-24
Fecha Fin: 2024-04-30

Líder del proyecto

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

TRL 4-5

Presupuesto del proyecto 213K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto The proposed research project fits into the broad programme of studying C*-algebras and groups dynamical origin, and is highly interdisciplinary in nature; it advances novel interactions among operator algebras, group theory, and topological dynamics. This project has two facets: First, I shall initiate the systematic study of a class of C*-algebras associated with algebraic semigroup actions, including example classes coming from group subshifts of finite type, modules over polynomial rings, rings of algebraic integers, and algebraic groups over number fields. After investigating structural properties of these C*-algebras, including ideal structure, pure infiniteness, Cartans, classifiability, and K-theory, I shall give a careful analysis of the Kubo--Martin--Schwinger (KMS) states for canonical time evolutions on these C*-algebras, and explore a mysterious connection between KMS states and K-theory that has manifested itself in the context of ax+b-semigroups. I will also look for connections between KMS states and entropy of algebraic actions. Second, I shall begin the study of the topological full groups associated with algebraic semigroup actions: I want to establish rigidity results and classify embeddings between these full groups, and I will study group-theoretic properties, including (co)homological finiteness conditions and the Haagerup property. I will then investigate Matui's AH conjecture in this setting, and explore whether non-sofic full groups exist. The project will strengthen my career by giving me the opportunity to work with leading experts in C*-algebras, group theory, and topological dynamics. It will also give me management skills by co-organising an international workshop, it will provide new possibilities for collaboration, and it will advance my ability as a researcher, so that I can obtain a permanent position at a research-oriented university. It will also open up new opportunities for collaboration between Glasgow, Lyon, Oslo, and the US.

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