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GeoMeG SIGNED

Geometry of Metric groups

Total Cost €

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EC-Contrib. €

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Partnership

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 GeoMeG project word cloud

Explore the words cloud of the GeoMeG project. It provides you a very rough idea of what is the project "GeoMeG" about.

university    group    appear    international    plan    abate    structure    questions    eth    links    sns    de    lipschitz    nash    permanent    5th    pde    distances    maps    limits    relation    degree    first    what    msri    obtaining    metric    theory    trailers    academy    advisor    minimality    asymptotics    regularity    corners    tackle    grow    allowed    trajectories    prestigious    graduation    steenrod    finland    implications    geometric    locally    harmonic    plans    subriemannian    spaces    mathematics    phd    he    position    kleiner    carnot    homogeneous    compact    nilpotent    fellow    net    subelliptic    lie    movement    curves    solutions    tangents    smoothness    asymptotic    differentiation    isometries    volume    theorem    hausdorff    prove    geodesics    pisa    groups    rectifiability    collaborations    park    lattice    distinguished    infinitesimal    perimeter    orsay    techniques    giorgi    examples    combination    fast    finite    isometric    geometry    embedding    yale    hilbert    pi    gromov    received    myers    truck   

Project "GeoMeG" data sheet

The following table provides information about the project.

Coordinator
UNIVERSITA DI PISA 

Organization address
address: LUNGARNO PACINOTTI 43/44
city: PISA
postcode: 56126
website: www.unipi.it

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Italy [IT]
 Total cost 1˙248˙560 €
 EC max contribution 1˙248˙560 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-STG
 Funding Scheme ERC-STG
 Starting year 2017
 Duration (year-month-day) from 2017-08-01   to  2022-07-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITA DI PISA IT (PISA) coordinator 493˙710.00
2    JYVASKYLAN YLIOPISTO FI (JYVASKYLA) participant 754˙850.00

Map

 Project objective

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.

 Publications

year authors and title journal last update
List of publications.
2020 Eero Hakavuori
Infinite Geodesics and Isometric Embeddings in Carnot Groups of Step 2
published pages: 447-461, ISSN: 0363-0129, DOI: 10.1137/19m1271166
SIAM Journal on Control and Optimization 58/1 2020-04-01
2019 Jesús A. Jaramillo, Enrico Le Donne, Tapio Rajala
Restricting open surjections
published pages: 1795-1798, ISSN: 1578-7303, DOI: 10.1007/s13398-018-0579-8
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 113/3 2020-03-05
2020 Luca Capogna, Enrico Le Donne
Conformal equivalence of visual metrics in pseudoconvex domains
published pages: , ISSN: 0025-5831, DOI: 10.1007/s00208-020-01962-1
Mathematische Annalen 2020-03-05
2019 Kai Rajala, Matthew Romney
Reciprocal lower bound on modulus of curve families in metric surfaces
published pages: 681-692, ISSN: 1239-629X, DOI: 10.5186/aasfm.2019.4442
Annales Academiae Scientiarum Fennicae Mathematica 44/2 2020-03-05
2020 Lorenzo Ruffoni, Francesca Tripaldi
Extending an Example by Colding and Minicozzi
published pages: 1028-1041, ISSN: 1050-6926, DOI: 10.1007/s12220-019-00177-4
The Journal of Geometric Analysis 30/1 2020-03-05
2019 Matthew Romney
Singular quasisymmetric mappings in dimensions two and greater
published pages: 479-494, ISSN: 0001-8708, DOI: 10.1016/j.aim.2019.05.022
Advances in Mathematics 351 2020-03-05
2019 Enrico Le Donne, Sean Li, Terhi Moisala
Infinite-Dimensional Carnot Groups and Gâteaux Differentiability
published pages: , ISSN: 1050-6926, DOI: 10.1007/s12220-019-00324-x
The Journal of Geometric Analysis 2020-03-05
2019 Rami Luisto
A Newman property for BLD-mappings
published pages: 135-146, ISSN: 1088-4173, DOI: 10.1090/ecgd/338
Conformal Geometry and Dynamics of the American Mathematical Society 23/8 2020-03-05
2017 Richard M. Aron, Jesús Angel Jaramillo, Enrico Le Donne
Smooth surjections and surjective restrictions
published pages: 525-534, ISSN: 1239-629X, DOI: 10.5186/aasfm.2017.4237
Annales Academiae Scientiarum Fennicae Mathematica 42 2020-03-05
2019 Andrei A. Ardentov, Enrico Le Donne, Yuri L. Sachkov
Sub-Finsler Geodesics on the Cartan Group
published pages: 36-60, ISSN: 1560-3547, DOI: 10.1134/s1560354719010027
Regular and Chaotic Dynamics 24/1 2019-05-15

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