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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... ver más

31/07/2023

UNIFR

1M€

Presupuesto del proyecto: 1M€

Líder del proyecto

UNIVERSITE DE FRIBOURG No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Ver 4 Participantes

Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2023-07-31

ERC-2016-STG: ERC Starting Grant

I+D

Cerrada hace 9 años

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Información adicional privada

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

4 Participantes

UNIFR

550.33K€ | Lider

SALICRU

747.58K€ | Participante

UNIVERSITY OFJYVASKYLAN

567.37K€ | Participante

UNIPI

130.86K€ | Participante

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Duración del proyecto: 76 meses Fecha Inicio: 2017-03-07
Fecha Fin: 2023-07-31

Líder del proyecto

UNIVERSITE DE FRIBOURG No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 1M€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto 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.

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