Title :

Some aspects of infinite-dimensional Geometry: Theory and Applications

English title :

Some aspects of infinite-dimensional Geometry: Theory and Applications

Author(s) :

Tumpach, Alice Barbara [Auteur]
Université de Lille

Thesis director(s) :

Stephane de Bièvre

Defence date :

2022-12-09

Jury president :

Juan-Carlos ALVAREZ-PAIVA
Esteban ANDRUCHOW
Stephan DE BIEVRE
Karl-Hermann NEEB
Cornelia VIZMAN
Tilmann WURZBACHER

Jury member(s) :

Juan-Carlos ALVAREZ-PAIVA
Esteban ANDRUCHOW
Stephan DE BIEVRE
Karl-Hermann NEEB
Cornelia VIZMAN
Tilmann WURZBACHER

Accredited body :

Lille University

Keyword(s) :

géometrie en dimension infinie
Groupes de Poisson-Lie banachiques
orbites coadjointes de dimension infinie
crochet de Poisson
Analyse des courbes et des surfaces
variétés Riemanniannes de dimension infinie

English keyword(s) :

Infinite-dimensional manifolds
Banach Poisson-Lie groups
infinite-dimensional coadjoint orbits
Poisson brackets
Shape analysis of curves and surfaces
infinite-dimensional Riemannian manifolds

HAL domain(s) :

Mathématiques [math]
Informatique [cs]

English abstract : [en]

We present some recent developments of infinite-dimensional Geometry, and show some applications in Shape Analysis. The first chapter is an introduction to the universal Teichmüller space and to its connexion to ...
Show more >We present some recent developments of infinite-dimensional Geometry, and show some applications in Shape Analysis. The first chapter is an introduction to the universal Teichmüller space and to its connexion to infinite-dimensional coadjoint orbits on one hand, and Shape Analysis via the fingerprint map on the other hand.Chapter II presents applications of infinite-dimensional Riemannian Geoemtry for Form Recognition and Shape Analysis of curves and surfaces.Chapter III is devoted to infinite-dimensional Poisson Geometry and its pathologies,notably we set the foundations of the theory of Banach Poisson--Lie groups.Show less >

Language :

Anglais

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL