IGOC
Financiado
Interactions between Groups Orbits and Cartans
Recently, we discovered that the notion of Cartan subalgebras builds bridges between C*-algebras, topological dynamics, and geometric group theory. The goal of this research project is to develop our understanding of this concept...
Recently, we discovered that the notion of Cartan subalgebras builds bridges between C*-algebras, topological dynamics, and geometric group theory. The goal of this research project is to develop our understanding of this concept in order to attack the following major open questions:
I. The UCT question
II. The Baum-Connes conjecture
III. The conjugacy problem for topological shifts
IV. Quasi-isometry rigidity for polycyclic groups
UCT stands for Universal Coefficient Theorem and is a crucial ingredient in classification. I want to make progress on the open question whether sufficiently regular C*-algebras satisfy the UCT, taking my joint work with Barlak as a starting point.
The Baum-Connes conjecture predicts a K-theory formula for group C*-algebras which has far-reaching applications in geometry and algebra as it implies open conjectures of Novikov and Kaplansky. My new approach to II will be based on Cartan subalgebras and the notion of independent resolutions due to Norling and myself.
Problem III asks for algorithms deciding which shifts are topologically conjugate. It has driven a lot of research in symbolic dynamics.
Conjecture IV asserts that every group quasi-isometric to a polycyclic group must already be virtually polycyclic. A solution would be a milestone in our understanding of solvable Lie groups.
To attack III and IV, I want to develop the new notion of continuous orbit equivalence which (as I recently showed) is closely related to Cartan subalgebras.
Problems I to IV address important challenges, so that any progress will result in a major breakthrough. On top of that, my project will initiate new interactions between several mathematical areas. It is exactly the right time to develop the proposed research programme as it takes up recent breakthroughs in classification of C*-algebras, orbit equivalence for Cantor minimal systems, and measured group theory, where measure-theoretic analogues of our key concepts have been highly successful.
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Duración del proyecto: 72 meses
Fecha Inicio: 2019-02-06
Fecha Fin: 2025-02-28
Fecha Fin: 2025-02-28
Línea de financiación: concedida
El organismo H2020 notifico la concesión del proyecto el día 2019-02-06
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
ERC-2018-COG:
ERC Consolidator Grant
Cerrada
hace 6 años
Presupuesto
El presupuesto total del proyecto asciende a
1M€
Líder del proyecto
UNIVERSITY OF GLASGOW
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
Perfil tecnológico
TRL
4-5
366.40K€ |
Participante