Scott Armstrong’s research webpage

I am currently working as a CNRS Directeur de recherche at Sorbonne University in the Laboratoire Jacques-Louis Lions (LJLL). I am on leave from my position as Professor of Mathematics at the Courant Institute of Mathematical Sciences at NYU.

My research focuses on mathematical physics, probability theory, and partial differential equations, with a particular emphasis on homogenization theory. This field investigates elliptic and parabolic equations, along with the associated diffusion processes, in highly heterogeneous environments. Recently, I have concentrated on developing rigorous renormalization group methods, inspired by homogenization techniques, and applying them to problems in mathematical physics.

Books/Monographs
  • S. Armstrong, T. Kuusi. Elliptic Homogenization from Qualitative to Quantitative. announcement | arxiv | github  
  • S. Armstrong, T. Kuusi and J.-C. Mourrat. Quantitative Stochastic Homogenization and Large-Scale Regularity. Grundlehren der mathematischen Wissenschaften vol. 352, Springer-Nature, Cham, 2019. full text
Selected Papers
  • S. Armstrong and T. Kuusi. Renormalization group and elliptic homogenization in high contrast. arXiv | blog post
  • S. Armstrong, A. Bou-Rabee and T. Kuusi. Superdiffusive central limit theorem for a Brownian particle in a critically-correlated incompressible random drift. arXiv | blog post | youtube
  • S. Armstrong and V. Vicol. Anomalous diffusion by fractal homogenization. Ann. PDE, to appear. arXiv | blog post | youtube
  • S. Armstrong and W. Wu. C^2 regularity of the surface tension for the \nabla\phi interface model. Comm. Pure Appl. Math., 75 (2022), 349-421. arXiv| journal 
  • S. Armstrong and P. Dario. Elliptic regularity and quantitative homogenization on percolation clusters. Comm. Pure Appl. Math., 71 (2018), 1717-1849. arXiv | journal
  • S. Armstrong, T. Kuusi and J.-C. Mourrat. The additive structure of elliptic homogenization. Invent. Math., 208 (2017), 999-1154. arXiv | journal
  • S. Armstrong and P. Cardaliaguet. Stochastic homogenization of quasilinear Hamilton-Jacobi equations and geometric motions. J. Eur. Math. Soc., 20 (2018), 797-864. arXiv | journal
  • S. N. Armstrong and C. K. Smart. Quantitative stochastic homogenization of convex integral functionals. Ann. Sci. Éc. Norm. Supér., 48 (2016), 423-481. arXiv | journal. 
    This paper received the 2017 SIAG/APDE Prize for most outstanding paper in PDE.

Complete list of publications

Links