Some aspects of infinite-dimensional Geometry: Theory and Applications

Alice Barbara Tumpach (1)

1 Université de Lille

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.

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

Mots clés: 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

Domaines: Mathématiques [math]; Informatique [cs]

Alice Barbara Tumpach. Some aspects of infinite-dimensional Geometry: Theory and Applications. Mathematics [math]. Lille University, 2022. ⟨tel-04052429⟩