Scott Armstrong’s research webpage

I am a Professor of Mathematics at the Courant Institute of Mathematical Sciences at NYU.

My research is in partial differential equations, probability theory, and mathematical physics. A particular focus is homogenization theory: the study of elliptic and parabolic equations and corresponding diffusion processes in highly heterogeneous environments.

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 V. Vicol. Anomalous diffusion by fractal homogenization. arXiv | blog post | youtube
  • S. Armstrong, T. Kuusi and C. Smart. Large-scale analyticity and unique continuation for periodic elliptic equations. Comm. Pure Appl. Math., 76 (2023), 73-113. arXiv | journal
  • 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, J.-C. Mourrat and C. Prange. Quantitative analysis of boundary layers in periodic homogenization. Arch. Ration. Mech. Anal., 226 (2017), 695-741. 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.
  • S. N. Armstrong and C. K. Smart. Quantitative stochastic homogenization of elliptic equations in nondivergence form, Arch. Ration. Mech. Anal., 214 (2014), 867-911. arXiv | journal

Complete list of publications

Links