GeoMeG: Description




The general goal of the project is to study Lie groups equipped with arbitrary distance functions and to develop an adapted geometric measure theory in the non-Riemannian settings.

The main focus is subRiemannian geometry, together with implications to control systems and nilpotent groups. SubRiemannian spaces, and especially Carnot groups, appear in various areas of mathematics, such as control theory, harmonic and complex analysis, subelliptic PDE's and geometric group theory.

The members of the team master methods coming from geometric measure theory, geometric analysis, and group theory; in particular, analysis on metric spaces and Lie group theory.



| Grant Agreement | University of Jyvskäylä Press Release |

People


Principal Investigator

Enrico Le Donne

| Personal website |

Post-Docs

Thibaut Dumont
Matthew Romney
Francesca Tripaldi


Ph.D. Students

Fares Essebei
Eero Hakavuori
Ville Kivioja
Terhi Moisala




Scientific Collaborators and Experts in the Field

See list

Jyväskylä Geometry Seminar


The Jyväskylä Geometry seminar is on Mondays afternoons
in the Department of Mathematics and Statistics.
The meeting is usually from 14:15 to 16:00 in room MaD 380.

Please, check in advance the calendar below.

No seminars are preview for the next weeks.



See all current Seminars | Analysis Seminar |

Past Seminars: 2017 | (older) |

Future Events



No events are planned for the next months.


Past Events
February/2018 Sub-Riemannian Geometry and Beyond
  

 


Recent Papers


We warmly thank the CVGMT Team for the support and
for hosting the following papers at CVGMT server.

  Blowups and blowdowns of geodesics in Carnot groups (2018)
 
E. Hakavuori, E. Le Donne   

We study infinitesimal and asymptotic properties of geodesics (i.e., isometric images of intervals) in Carnot groups equipped with arbitrary sub-Finsler metrics. We show that tangents of geodesics are geodesics in some groups of lower nilpotency step. Namely, every blowup curve of every geodesic in every Carnot group is still a geodesic in the group modulo its last layer. With the same approach, we also show that blowdown curves of geodesics in sub-Riemannian Carnot groups are contained in subgroups of lower rank. This latter result can be extended to rough geodesics.


| See the complete list of papers |

 

Open Positions


Please, contact the PI if you are interested to do a Ph.D. or a postdoc
in the framework of GeoMeG ERC project.

New positions will be open in the next years.


Prof. Enrico Le Donne

 

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