Frédéric Rochon

Research

In geometry and mathematical physics, singular and non-compact spaces are ubiquitous. Ideally, one would like to be able to use results of analysis as if they were smooth compact spaces, but this is not always possible. My research is in fact about studying and developing geometric analysis on such spaces. I particularly like to use manifolds with corners to resolve singularities or to describe in a conceptual way certain asymptotical behaviors at infinity. This gives rise to various applications, for instance for the geometry of moduli spaces, which are often singular or non-compacts, or for certain types of geometries like hyperbolic geometry or Kähler-Einstein geometry.

Some talks:

Quasi-fibred boundary pseudodifferential operators (BIRS, May 2021)

Torsion on hyperbolic manifolds of finite volume (BIRS, April 2018)

QAC Calabi-Yau manifolds (Oaxaca, December 2016)

Renormalized volume on the Teichmuller space of punctured Riemann surfaces (Newton Instittute, July 2015)

An index theorem via resolvent estimates (BIRS, November 2014)