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math.DG2025
On longitudinal differential operators and Nash blowups
Ruben Louis
In this short note, we describe the Helffer-Nourrigat cone of a singular foliation in terms of the Nash algebroid associated to the foliation. Along the way, we show that the Helff…
math.DG2024
An invitation to singular foliations
Camille Laurent-Gengoux, Ruben Louis, Leonid Ryvkin
These lecture notes attempt to invite the reader towards the theory of singular foliations, both smooth and holomorphic. In addition to a systematic review of the foundations, and…
math.DG2024
On Nash resolution of (singular) Lie algebroids
Ruben Louis
Any Lie algebroid admits a Nash-type blow-up that sits in a nice short exact sequence of Lie algebroids $0\rightarrow K\rightarrow \mathrm{Nash}(A)\rightarro…