Francesco Di Plinio

Current/upcoming travel

• Evolution Equations and Dynamical Systems, a tribute to Vittorino Pata, Milano, Nov. 27, 2026 https://www.mate.polimi.it/events/VIS60/?utm_source=chatgpt.com

What's new?

• 7 October 2026 — Sparse domination modulo polynomials
  I develop a sparse domination theory that retains local polynomial cancellation, and characterize the Calderón–Zygmund operators satisfying these bounds through polynomial testing conditions. Applications include weighted Hardy–Sobolev estimates with linear A∞ dependence and pointwise bounds by Riesz potentials.

• 1 October 2026 — Maximal directional singular integrals
  With Ioannis Parissis, I survey maximal directional averages and singular integrals, from lacunary sets and vector fields to algebraic families in higher dimensions. The article connects these questions with Kakeya–Nikodym phenomena, differentiation and the Carleson operator, and collects open problems.

• 6 March 2026 — The planar Coleman–Gurtin model with Beltrami conductivity
  I study the planar heat equation with memory and rough anisotropic diffusion encoded by a Beltrami coefficient. The paper establishes instantaneous regularization and, under Sobolev regularity of the coefficient, finite-dimensional global and exponential attractors. Published in DCDS-S 26 (2026), 188–215.

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Grant Support

• CO-PI, Fondo Ricerca di Ateneo UNINA 2023-26 (with S. Almi, U. De Maio, C. Leone)

• PI, NSF Grant NSF-DMS-2054863, project “Symmetry Parameter Analysis of Singular Integrals” 2021- 2024: URL

•  PI, NSF Grant NSF-DMS-1800628/2000510, project  “Singular Integrals with Modulation or Rotational Symmetry" 2018-2022: $179,972.
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•  PI, NSF Grant NSF-DMS-1650810, project  “Endpoint Behavior of Modulation Invariant Singular Integrals”,  2015- 2019: $151,237 URL