Innovating Works

GeoMeG

Financiado
Geometry of Metric groups
What are the best trajectories to park a truck with several trailers? How fast can a lattice grow? These are some of the questions studied in this project because both the infinitesimal control structure of movement of a truck and... What are the best trajectories to park a truck with several trailers? How fast can a lattice grow? These are some of the questions studied in this project because both the infinitesimal control structure of movement of a truck and the asymptotic geometry of a (nilpotent) lattice are examples of metric groups: Lie groups with homogeneous distances. The PI plans to study geometric properties of metric groups and their implications to control systems and nilpotent groups. In particular, the plan is to exploit the relation between the regularity of distinguished curves, sets, and maps in subRiemannian groups, volume asymptotics in nilpotent groups, and embedding results. The general goal is to develop an adapted geometric measure theory. SubRiemannian spaces, and in particular Carnot groups, appear in various areas of mathematics, such as control theory, harmonic and complex analysis, asymptotic geometry, subelliptic PDE's and geometric group theory. The results in this project will provide more links between such areas. The PI has developed a net of high-level international collaborations and obtained several results via a combination of analysis on metric spaces (differentiation of Lipschitz maps, tangents of measures, and Gromov-Hausdorff limits) and the theory of locally compact groups (Lie group techniques and the solutions of the Hilbert 5th problem). This allowed the PI to solve a number of open problems in the field, such as the analogue of Myers-Steenrod theorem on the smoothness of isometries, the analogue of Nash isometric embedding and the non-minimality of curves with corners. Some of the next aims are to establish an analogue of the De Giorgi's rectifiability result for finite-perimeter sets and prove the smoothness of geodesics, a 30-year-old open problem. The goal of this project is to tackle them, together with many more related questions. The PI received his first degree at SNS Pisa (advisor: M.Abate) and his PhD from Yale University (advisor: B.Kleiner). Before obtaining a permanent position only three years after graduation, he was at ETH, Orsay, and MSRI. He received the prestigious position of research fellow of the Academy of Finland. ver más
31/07/2023
UNIFR
1M€
Duración del proyecto: 76 meses Fecha Inicio: 2017-03-07
Fecha Fin: 2023-07-31

Línea de financiación: concedida

El organismo H2020 notifico la concesión del proyecto el día 2023-07-31
Línea de financiación objetivo El proyecto se financió a través de la siguiente ayuda:
ERC-2016-STG: ERC Starting Grant
Cerrada hace 9 años
Presupuesto El presupuesto total del proyecto asciende a 1M€
Líder del proyecto
UNIVERSITE DE FRIBOURG No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico TRL 4-5