About

Professor Jill Pipher's primary area of research is harmonic analysis and its applications to elliptic partial differential equations with non-smooth coefficients. She also has a research interest in cryptography, particularly lattice-based cryptography. Her work bridges advanced mathematical theories and practical applications, contributing to both the understanding of complex differential equations and the development of cryptographic methods. For more detailed information about her research and academic contributions, additional resources such as her CV and Brown University Research page are available.

Research topics

• Mathematical analysis
• Mathematics
• Combinatorics
• Physics
• Quantum mechanics
• Pure mathematics
• Applied mathematics
• Law
• Statistics

Selected publications

• Localization and interpolation of parabolic $L^p$ Neumann problems

  ArXiv.org · 2026-01-18

  articleOpen accessSenior author

  We show a localization estimate for local solutions to the parabolic equation $-\partial_t u+\mbox{div} (A\nabla u)=0$ with zero Neumann data, assuming that the $L^p$ Neumann problem and $L^{p'}$ Dirichlet problem for the adjoint operator are solvable in a Lipschitz cylinder for some $p\in(1,\infty)$. Using this result, we establish the solvability of the Neumann problem in the atomic Hardy space for parabolic operators with bounded, measurable, time-dependent coefficients, and hence obtain the extrapolation of solvability of the $L^p$ Neumann problem.

  PublisherOA PDF

• Localization and interpolation of parabolic $L^p$ Neumann problems

  arXiv (Cornell University) · 2026-01-18

  preprintOpen accessSenior author

  We show a localization estimate for local solutions to the parabolic equation $-\partial_t u+\mbox{div} (A\nabla u)=0$ with zero Neumann data, assuming that the $L^p$ Neumann problem and $L^{p'}$ Dirichlet problem for the adjoint operator are solvable in a Lipschitz cylinder for some $p\in(1,\infty)$. Using this result, we establish the solvability of the Neumann problem in the atomic Hardy space for parabolic operators with bounded, measurable, time-dependent coefficients, and hence obtain the extrapolation of solvability of the $L^p$ Neumann problem.

  PublisherDOI

• An endpoint estimate for product singular integral operators on stratified Lie groups

  Canadian Journal of Mathematics · 2025-01-27 · 1 citations

  articleOpen accessSenior author

  Abstract We establish hyperweak boundedness of area functions, square functions, maximal operators, and Calderón–Zygmund operators on products of two stratified Lie groups.

  PublisherOA PDFDOI

• The $L^p$ regularity problem for parabolic operators with transversally independent coefficients

  ArXiv.org · 2025-09-08

  preprintOpen access

  In this paper, we fully resolve the question of whether the Regularity problem for the parabolic PDE $\partial_tu - \mbox{div}(A\nabla u)=0$ on the domain $\mathbb R^{n+1}_+\times\mathbb R$ is solvable for some $p\in (1,\infty)$ under the assumption that the matrix $A$ is elliptic, has bounded and measurable coefficients and its coefficients are independent of the spatial variable $x_{n+1}$ (which is transversal to the boundary). We prove that for some $p_0>1$ the Regularity problem is solvable in the range $(1,p_0)$. An analogous result for the Dirichlet problem has been considered earlier by Auscher, Egert and Nyström, however the Regularity problem represents an additional step up in difficulty. In the elliptic case, the analog of the question considered here was resolved for both Dirichlet and Regularity problems by Hofmann, Kenig, Mayboroda and Pipher. The main result of this paper complements a recent work of two of the authors with L. Li showing solvability of the parabolic Regularity problem for data in some $L^p$ spaces when the coefficients satisfy a natural Carleson condition (which is a parabolic analog of the so-called DKP-condition).

  PublisherOA PDFDOI

• Commutator estimates for Haar shifts with general measures

  Journal of Functional Analysis · 2025-03-21 · 1 citations

  articleCorresponding
  PublisherDOI

• Commutator estimates for Haar shifts with general measures

  arXiv (Cornell University) · 2024-09-02

  preprintOpen access

  We study $L^p(μ)$ estimates for the commutator $[H,b]$, where the operator $H$ is a dyadic model of the classical Hilbert transform introduced in \cite{arXiv:2012.10201,arXiv:2212.00090} and is adapted to a non-doubling Borel measure $μ$ satisfying a dyadic regularity condition which is necessary for $H$ to be bounded on $L^p(μ)$. We show that $\|[H, b]\|_{L^p(μ) \rightarrow L^p(μ)} \lesssim \|b\|_{\mathrm{BMO}(μ)}$, but to {\it characterize} martingale BMO requires additional commutator information. We prove weighted inequalities for $[H, b]$ together with a version of the John-Nirenberg inequality adapted to appropriate weight classes $\widehat{A}_p$ that we define for our non-homogeneous setting. This requires establishing reverse Hölder inequalities for these new weight classes. Finally, we revisit the appropriate class of nonhomogeneous measures $μ$ for the study of different types of Haar shift operators.

  PublisherOA PDFDOI

• The $L^p$ regularity problem for parabolic operators

  arXiv (Cornell University) · 2024-10-31

  preprintOpen accessSenior author

  In this paper, we fully resolve the question of whether the Regularity problem for the parabolic PDE $-\partial_tu + \mbox{div}(A\nabla u)=0$ on a Lipschitz cylinder $\mathcal O\times\mathbb R$ is solvable for some $p\in (1,\infty)$ under the assumption that the matrix $A$ is elliptic, has bounded and measurable coefficients and its coefficients satisfy a natural Carleson condition (a parabolic analog of the so-called DKP-condition). We prove that for some $p_0>1$ the Regularity problem is solvable in the range $(1,p_0)$. We note that answer to this question was not known even in the small Carleson case, that is, when the Carleson norm of coefficients is sufficiently small. In the elliptic case the analogous question was only fully resolved recently independently by two groups, with two very different methods: one involving two of the authors and S. Hofmann, the second by M. Mourgoglou, B. Poggi and X. Tolsa. Our approach in the parabolic case is motivated by that of the first group, but in the parabolic setting there are significant new challenges.

  PublisherOA PDFDOI

• Boundary Value Problems for Elliptic Operators Satisfying Carleson Condition

  Trends in mathematics · 2024-01-01

  book-chapterSenior author
  PublisherDOI

• Balanced measures, sparse domination and complexity-dependent weight classes

  Mathematische Annalen · 2024-08-28 · 3 citations

  article
  PublisherDOI

• Boundary Value Problems for Elliptic Operators Satisfying Carleson Condition

  Vietnam Journal of Mathematics · 2023-10-21 · 2 citations

  articleSenior authorCorresponding
  PublisherDOI

Recent grants

• Harmonic Analysis and Linear Elliptic Equations

  NSF · $173k · 2006–2009

• Harmonic Analysis and the Theory of Elliptic Measure

  NSF · $435k · 2009–2013

Frequent coauthors

• Jeffrey Hoffstein

  Providence College

  69 shared

• Joseph H. Silverman

  57 shared

• Martin Dindoš

  43 shared

• Carlos E. Kenig

  University of Chicago

  29 shared

• Gregory C. Verchota

  Syracuse University

  28 shared

• William Whyte

  Qualcomm (United States)

  20 shared

• Camil Muscalu

  Romanian Academy

  19 shared

• Stefanie Petermichl

  19 shared

Awards & honors

• Elisha Benjamin Andrews Professor of Mathematics, Brown Univ…
• Founding Director, ICERM