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).
Publications
Preprints
- C. Cren, A transverse index theorem in the calculus of filtered manifolds, preprint 2022, to appear in Journal of Functional Analysis.
- C. Cren, Filtered Calculus and crossed products by R-actions, 2023, submitted.
- C. Cren, Transverse parabolic structures and transverse BGG sequences, 2023, submitted. Find a complete list on ArXiV or HAL. You can also use my ORCID: 0000-0001-9217-4953.
Others
- PhD Thesis (2023) Pseudodifferential calculus on filtered manifolds and applications to geometry and harmonic analysis, under supervision of Jean-Marie Lescure.
- Masters (M2) Thesis (2020, in French) Groupoïdes de déformation et calcul pseudo-différentiel inhomogène, under supervision of Georges Skandalis.
- Masters (M1) Thesis (2018, in French) Metriques de Klein et généralisations sur l'espace projectif réel, under supervision of Charles Boubel.
Teachings
2023-2024:
- SoSe:
- Functional analysis (teaching assistant, course by Christopher Wulff).
- Latex Kurs (lecturer, in August 2024).
- WiSe:
- Introduction to algebraic geometry (teaching assistant, course by Evelina Viada).
- Onbourding tutorial in non-commutative geometry
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. A list including those I only attended can be found on my CV- April 2024: CIRM (Marseille), Group operator algebras and Non commutative geometry conference.
- March 2024: Sichuan University Chengdu, Algebraic, analytic, geometric structures emerging from quantum field theory school and workshop (mini-course + research talk).
- December 2023: Université de Lorraine Metz, GDR Géométrie Non-Commutative Arbre de Noël conference.
- June 2023: Université de Lorraine Metz, Théorie de Lie, Géométrie et Analyse seminar.
- March 2023: Athens, Noncommutative Geometry and Representation Theory conference.
- September 2022: Université Paris-Cité, Operator Algebras seminar.
- June 2022: Cortona, Operators in Topology, Geometry, and Representation Theory conference.
- June 2022: Caen, Non-Commutative geometry GDR conference.
- May 2022: Dartmouth College, Functional Analysis Seminar