Generated by All in One SEO v5.0.1.1, this is an llms.txt file, used by LLMs to index the site. # Scott Armstrong CNRS - Sorbonne Université ## Sitemaps - [XML Sitemap](https://www.scottnarmstrong.com/sitemap.xml): Contains all public & indexable URLs for this website. ## Posts - [Scott Armstrong's Blog](https://www.scottnarmstrong.com/blog/) - Scott Armstrong's Research Blog - [Formalizing Stochastic Homogenization in Lean](https://www.scottnarmstrong.com/2026/06/formalizing-stochastic-homogenization-in-lean/) - Tuomo Kuusi and I have formalized some of the main results of our recent paper on quantitative stochastic homogenization in the Lean 4 proof assistant. The repository is available here. In that paper we developed a coarse-graining theory for elliptic equations in divergence form, which was applied to obtain quantitative stochastic homogenization results in the - [Formalizing De Giorgi-Nash-Moser theory in Lean](https://www.scottnarmstrong.com/2026/04/formalizing-de-giorgi-nash-moser-theory-in-lean/) - Julia Kempe and I have just completed a Lean 4 formalization of De Giorgi--Nash--Moser theory. We formalized the full slate of interior regularity statements for weak solutions of divergence-form elliptic equations with merely bounded measurable (and not necessarily symmetric) coefficients, including local boundedness, the weak Harnack and Harnack inequalities, and finally interior Hölder regularity. The - [Power-law superdiffusion in self-similar incompressible random flows](https://www.scottnarmstrong.com/2026/01/superdiffusivity-anomalous-regularization/) - [latexpage] Ahmed Bou-Rabee, Tuomo Kuusi, and I have just uploaded our paper "Superdiffusion and anomalous regularization in self-similar random incompressible flows" to the arXiv. In it we consider the behavior of a diffusion in a multiscale, random divergence-free drift. We prove that the variance of the displacement of the particle grows superlinearly in time with - [Renormalization group and quantitative homogenization in high contrast](https://www.scottnarmstrong.com/2024/05/high-contrast-homogenization/) - [latexpage] Tuomo Kuusi and I have just posted our paper "Renormalization group and elliptic homogenization in high contrast" to the arXiv. The paper is about quantitative homogenization of the elliptic equation \begin{equation} \label{e.a} -\nabla \cdot \mathbf{a}(x) \nabla u = 0 \end{equation} where $\mathbf{a}:\mathbb{R}^d \to \mathbb{R}^{d\times d}$ is a matrix-valued coefficient field. In our setup, we - [A superdiffusive invariance principle by iterative quantitative homogenization](https://www.scottnarmstrong.com/2024/04/superdiffusive-clt/) - [latexpage] We have just uploaded our paper, joint with Ahmed Bou-Rabee and Tuomo Kuusi, titled "Superdiffusive central limit theorem for a Brownian particle in a critically-correlated incompressible random drift," to the arXiv. The results in this paper were recently announced by Ahmed in several public talks, including this one at the Fields Institute. The paper - [Anomalous diffusion by fractal homogenization](https://www.scottnarmstrong.com/2023/05/anomalous-diffusion-fractal-homogenization/) - [latexpage] Vlad Vicol and I have just uploaded our paper "Anomalous diffusion by fractal homogenization" to the arxiv. It contains results previously announced last June at the "Probability and Mathematical Physics" conference in Helsinki and in subsequent seminar talks by both of us since then. (A recording of my Helsinki talk can be found here.) - [Elliptic Homogenization from Qualitative to Quantitative](https://www.scottnarmstrong.com/2022/10/elliptic-homogenization-from-quantitative-to-qualitative/) - A new introductory text by Armstrong & Kuusi on stochastic homogenization for elliptic PDE, covering the qualitative and quantitative theories. ## Pages - [Scott Armstrong's research webpage](https://www.scottnarmstrong.com/) - [latexpage] Scott Armstrong's research webpage This paper received a 2026 Frontier of Science Award . S. Armstrong, A. Bou-Rabee and T. Kuusi. Superdiffusive central limit theorem for a Brownian particle in a critically-correlated incompressible random drift. Invent. Math., to appear. arXiv | Quanta | blog post | youtube S. Armstrong and V. Vicol. Anomalous diffusion by - [Lean Repositories](https://www.scottnarmstrong.com/lean-repositories/) - [latexpage] Lean repositories DeGiorgi (with Julia Kempe). Formalizes De Giorgi–Nash–Moser theory for uniformly elliptic divergence-form equations with bounded measurable coefficients: local boundedness, weak and strong Harnack inequalities, and Hölder regularity. Includes supporting developments in Sobolev spaces and weak derivatives. CoarseGraining (with Tuomo Kuusi). Formalizes coarse-graining theory for elliptic equations, including quenched homogenization estimates for isotropic - [Publications and Preprints](https://www.scottnarmstrong.com/publications/) - [latexpage] Preprints S. Armstrong and J. Kempe. Formalization of De Giorgi-Nash-Moser Theory in Lean. arXiv | github | blog post | Lean formalization S. Armstrong, A. Bou-Rabee and T. Kuusi. Superdiffusion and anomalous regularization in self-similar random incompressible flows. arXiv | blog post | youtube | Lean formalization S. Armstrong, B. Avelin, C. De Filippis, T. Kuusi - [CV](https://www.scottnarmstrong.com/cv/) - Scott N. Armstrong - Short CV Academic Positions Sorbonne Université CNRS directeur de recherche, 2024-present. The Courant Institute of Mathematical Sciences, New York University Professor of Mathematics, 2019-present (currently on leave). Associate Professor of Mathematics, 2016-2019. Université Paris Dauphine-PSL CNRS chargé de recherche, 2012-2016. The University of Wisconsin-Madison Assistant Professor, 2011-2012. The University of - [Contact Info](https://www.scottnarmstrong.com/contact/) - Contact Information Mailing Address: Courant Institute of Mathematical Sciences New York University 251 Mercer St New York, NY 10012 Offices: Warren Weaver Hall, room 616 Laboratoire Jacques-Louis Lions 15-16.104 Emails: scottnarmstrong@gmail.com (preferred) scottarmstrong@nyu.edu scott.armstrong@sorbonne-universite.fr ## Posts - [Attribution](https://www.scottnarmstrong.com/attribution/) - This site has been created with the help of many different people and companies. This site was built on a powerful, Inspirations based web builder called BoldGrid. It is running on WordPress, the most popular content management software online today. Web hosting support is provided by DreamHost. 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