Mathieu Dutour

About me

I am currently a postdoctoral fellow at the University of Alberta, in Edmonton, working alongside Manish Patnaik on interactions between loop groups and Arakelov geometry.

Before that, I was a Ph.D. student at Sorbonne Université, in Paris, where I worked under the supervision of Gerard Freixas i Montplet on Arakelov geometry for singular metrics, and more precisely on obtaining a Deligne-Riemann-Roch isometry for flat unitary holomorphic vector bundles over modular curves.

My main mathematical interest is Arakelov geometry, a relatively recent discipline which involves many other interesting areas of research, such as complex and algebraic geometry, number theory, spectral theory, functional analysis, to name but a few.

More recently, I re-discovered the theory of Lie and Kac-Moody algebras, which I had partly learned years ago, when I started studying loop groups. The interaction between those and Arakelov geometry, although surprising at first, ends up being perfectly natural, in view of recent works on pro-Hermitian vector bundles and theta invariants.

Here, you can find my most recent research project in English, and a French version of it.

Email address:

Questions and comments are welcome! Also, please let me know if there are any dead links.

Research articles and preprints

Theta-finite pro-Hermitian vector bundles from loop groups elements

This talk was held on November 28th, 2022 for the Number Theory and Combinatorics Seminar at the University of Lethbridge, in Alberta, Canada.

Sound level drops at around 7:00 due to some technical issue, but the talk can still be heard.


Note: Every available video recording of my talks can be accessed in the section "Research presentations" below.

Quillen metrics on modular curves

This talk was held on November 6th, 2021, during the Alberta Number Theory Days at Banff International Research Station, in Alberta, Canada.


Note: Every available video recording of my talks can be accessed in the section "Research presentations" below.

Research presentations


Version française.

Education and research positions

The base template used for the pdf versions of the CV is available here.

Organization of seminars and other events


Research internships