SuPerGRandMa
Financiado
Hyperbolic surfaces and large random maps
The main purpose of this proposal is to explore random planar metrics. Two canonical models of random continuum surfaces have been introduced in the past decade, namely the Brownian sphere obtained as the scaling limit of uniform...
The main purpose of this proposal is to explore random planar metrics. Two canonical models of random continuum surfaces have been introduced in the past decade, namely the Brownian sphere obtained as the scaling limit of uniform random planar triangulations, and the Liouville Quantum Gravity metric obtained formally from the exponential of the Gaussian free field on the sphere. Our objective is to broaden our understanding of random planar metrics to the case of metrics with holes or hubs, and to the causal (when a time dimension is singled out) paradigm. We also plan on studying random maps in high genus and to connect to models of 2-dimensional hyperbolic geometry such as the Brook–Makover model, random pants decompositions or Weil–Petersson random surfaces.
We believe that the tools developed in the context of random planar maps, such as the systematic use of the spatial Markov property, the utilization of random trees to decompose and explore the surfaces, or the fine study of geodesic coalescence can be successfully applied to the aforementioned models. We expect spectacular results and we hope to reinforce the connections between those very active fields of mathematics. This proposal should give rise to exceptionally fruitful interactions between specialists of different domains such as probability theory, two-dimensional hyperbolic geometry, and theoretical physics, as well as mathematicians coming from other areas, in particular from combinatorics.
To ensure the best chances of success for the proposed research, we will rely on the unique environment of University Paris-Saclay and neighboring institutions.
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Duración del proyecto: 67 meses
Fecha Inicio: 2023-03-16
Fecha Fin: 2028-10-31
Fecha Fin: 2028-10-31
Línea de financiación: concedida
El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2023-03-16
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
ERC-2022-COG:
ERC CONSOLIDATOR GRANTS
Cerrada
hace 2 años
Presupuesto
El presupuesto total del proyecto asciende a
2M€
Líder del proyecto
UNIVERSITE PARISSACLAY
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
Perfil tecnológico
TRL
4-5