Contributions to infinite dimensional geometry and analysis

2022/05/03 by Magnot, Jean-Pierre
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2205.02929

Abstract

The works prsented in this habilitation thesis can be gathered in six themes. Works on the implicit function theorem and the geometry of numerical schemes. On the existence of an exponential map on an infinite dimensioal Lie group. Holonomy and Ambrose-Singer theorem for connections on infinite dimensional principal bundles. Results on integration theory and discretized Yang-Mills theory. Works on non-formal pseudo-differential operators (PDOs), ζ-renormalized traces, manifolds of maps and related topics. Works on the Kadomtsev-Petsviashvili (KP) hierarchy.

Related

• Mathematical results inspired by physics
• Painleve' transcendents and two-dimensional topological field theory
• Differential Geometry, Lie Groups and Symmetric Spaces over General Base Fields and Rings
• Some very low-dimensional algebraic topology
• Geometry of moduli spaces of meromorphic connections on curves, Stokes data, wild nonabelian Hodge theory, hyperkahler manifolds, isomonodromic deformations, Painleve equations, and relations to Lie theory