My name is John Hoffman. Since the fall of 2023, I have been a Postdoctoral researcher in the mathematics department at Florida State University under the supervision of Sasha Reznikov. My research lies at the intersection of harmonic analysis, partial differential equations, and geometric measure theory. I am generally interested in notions of quantitative rectifiability, and the relationships between analytic, geometric, and PDE-related properties of sets. I completed my PhD in the spring of 2023 at the University of Missouri under the supervision of Steve Hofmann.
Here is my cv.
Publications:
Square Functions Controlling Smoothness and Higher-Order Rectifiability, to appear in Mathematische Annalen, arxiv.org/pdf/2410.11724 .
Corona decompositions for parabolic uniformly rectifiable sets. Joint with Simon Bortz, Steve Hofmann, Kaj Nyström, and José Luis Luna García. Journal of Geometric Analysis, 2023 arXiv .
Carleson measure estimates for caloric functions and parabolic uniformly rectifiable sets. Joint with Simon Bortz, Steve Hofmann, Kaj Nyström, and José Luis Luna García, Analysis & PDE, 2023 arXiv .
Coronizations and big pieces in metric spaces. Joint with Simon Bortz, Steve Hofmann, Kaj Nyström, and José Luis Luna García. Annales de l’Institut Fourier, 2022. arXiv
On big pieces approximations of parabolic hypersurfaces. Joint with Simon Bortz, Steve Hofmann, Kaj Nyström, and José Luis Luna García, Annales Fennici Mathematici, 2022. arXiv
Parabolic singular integrals with nonhomogeneous kernels Joint with Simon Bortz, Steve Hofmann, Kaj Nyström, and José Luis Luna García arXiv:2103.12830v1 arXiv