SRS
Financiado
Stationary Random Subgroups
The notion of invariant random subgroups (IRS) has proven extremely useful during the last decade, particularly to the study of asymptotic invariants of lattices. However, the scope of problems that one can investigate when restri...
The notion of invariant random subgroups (IRS) has proven extremely useful during the last decade, particularly to the study of asymptotic invariants of lattices. However, the scope of problems that one can investigate when restricting to invariant measures (on the space of subgroups) is limited. It was recently realised that the notion of stationary random subgroups (SRS), which is much more general, is still extremely powerful and opens up new paths to attacking problems that previously seemed to be out of our reach.
Notably, the notion of stationary random subgroups has turned out to be a wonderful new tool in the analysis of discrete subgroups of infinite co-volume, and, in particular, thin subgroups of arithmetic groups. A few months ago M. Fraczyk and I proved, using SRS, the following conjecture of Margulis: Let G be a higher rank simple Lie group and Λ ⊂ G a discrete subgroup. Then the orbifold Λ\G/K has finite volume if and only if it has bounded injectivity radius. This is a far-reaching generalisation of the celebrated Normal Subgroup Theorem of Margulis, and while it is new even for subgroups of lattices, it is completely general.
One of the main problems we wish to solve is the variant of the Schoen–Yau Conjecture postulated by Margulis; namely, that higher rank, locally symmetric manifolds Λ\G/K of infinite volume are not Liouville. A positive answer would have many applications in the theory of discrete subgroups of Lie groups. Some exiting applications are possible using partial results.
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Duración del proyecto: 72 meses
Fecha Inicio: 2022-04-27
Fecha Fin: 2028-04-30
Fecha Fin: 2028-04-30
Línea de financiación: concedida
El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2022-04-27
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
ERC-2021-ADG:
ERC ADVANCED GRANTS
Cerrada
hace 3 años
Presupuesto
El presupuesto total del proyecto asciende a
2M€
Líder del proyecto
WEIZMANN INSTITUTE OF SCIENCE
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
Perfil tecnológico
TRL
4-5