About me

My name is Clément Cren. I am a postdoc at the Mathematisches Institut of Göttingen Universität. Before that I was a PhD student at Université Paris-Est Créteil. I am part of RTG 2491 Fourier Analysis and Spectral Theory.

Research interests

I work in the field of non-commutative geometry. The idea, following the philosophy of Alain Connes, is to replace spaces with ill behaved topology (manifolds with boundary or corners, orbifolds, leaf space of a foliation...) by non-commutative algebras (the ones that happen to be commutative correspond to the well behaved spaces following Gelfand and Naimark). This change of paradigm corresponds to a "quantum" point of view. We replace the notion of space by operators on a Hilbert space (a C*-algebra). Because of that, the tools I use are related to problems arising from physics such as quantization or semi-classical analysis (going from classical to quantum and vice-versa). I am interested in these problems through the prism of pseudodifferential operators theory and Lie groupoids. In my thesis I focused on a pseudofifferential calculus suited for filtered manifolds (e.g. contact). I used a tangent groupoid approach to generalize results known for the usual pseudodifferential calculus. I now want to also apply these techniques to the aforementioned problems (e.g. geometric quantization). Part of my work focuses on Toeplitz operators: the link they have with C*-algebras of nilpotent groups and with symplectic/contact geometry.

Papers

Published papers

Preprints

Others

Teachings

2025-2026:

2024-2025:

2023-2024:

Previous teachings: see my detailed CV.

Talks at conferences and seminars

This is the list of the conferences and seminars where I have given a talk and also includes the upcoming ones. A list including the conferences I also attended can be found on my CV

Contact