arXiv subjects

Pierre Houédry

Publications and source records attributed to Pierre Houédry.

3 recordsLinked to original sources

arXiv2026

Twisted calculus in several variables

In this paper, we introduce novel concepts and establish a formal framework for twisted differential operators in the context of several variables. The focus is on twisted coordinates within Huber rings, which facilitate the construction of diverse rings of twisted differential operators. We establish an equivalence between modules equipped with twisted connections and those endowed with actions of twisted derivatives. Furthermore, we examine the convergence properties of twisted differential operators under specific conditions. As one of the main results, we extend the confluence theorem of Le Stum and Quirós to several variables. This work aligns with the ongoing advancements in $p$-adic Hodge cohomology and prismatic cohomology.

math.AG↗

arXiv2026

Spherical Harmonic Optimal Transport: Application to Climate Models Comparisons

Optimal transport provides a powerful framework for comparing measures while respecting the geometry of their support, but comes with an expensive computational cost, hindering its potential application to real world use cases. On manifolds, convolutional algorithms based on the heat kernel have been proposed to alleviate this cost, but their theoretical properties remain largely unexplored. We establish that the heat kernel cost converges to the optimal transport cost as time vanishes in the balanced and unbalanced cases. In the specific case of the 2-sphere $\mathbb{S}^2$, we ensure that the associated Sinkhorn divergences retains the desirable geometric and analytic properties of classical optimal transport discrepancies. Moreover, we leverage the harmonic structure of the sphere to derive a fast Sinkhorn algorithm, requiring only $\mathcal{O}(n)$ memory and $\mathcal{O}(n^{3/2})$ time per iteration, with fully dense GPU-friendly operations. We validate its computational efficiency on synthetic data, and discuss its potential use in the evaluation of global climate models, providing both spatial and seasonal insights into models performances.

cs.LG↗

arXiv2024

Twisted differential operators in several variables

We introduce new concepts in order to develop a general formalism for twisted differential operators in several variables. We investigate the notion of twisted coordinates on Huber rings that allows us to build various rings of twisted differential operators and compare them. We show that there exists an equivalence between modules endowed with a twisted connection and modules endowed with an action of the twisted derivatives. This work is in line with the recent developments in $p$-adic Hodge cohomology and prismatic cohomology.

math.AG↗