Camil Muscalu

About

Camil Muscalu is a professor in the Department of Mathematics at Cornell University. He holds a Ph.D. from Brown University, obtained in 2000. His research focuses on harmonic analysis and partial differential equations, particularly the study of Fourier series and their applications to understanding physical phenomena. Muscalu is interested in the process of discovery and analysis of new mathematical objects, such as iterated Fourier series, and their deep connections to other areas of mathematics, including the theory of multiple zeta functions, number theory, and physics. His work involves exploring fundamental questions like the convergence of these series almost everywhere and their relation to natural phenomena, contributing to the broader understanding of harmonic analysis and its applications.

Research topics

• Computer Science
• Mathematics
• Law
• Geometry
• Combinatorics
• Pure mathematics

Selected publications

• Multiple vector-valued inequalities via the helicoidal method

  Analysis & PDE · 2016-12-11 · 57 citations

  articleOpen accessSenior author

  We develop a new method of proving vector-valued estimates in harmonic analysis, which we call “the helicoidal method”. As a consequence of it, we are able to give affirmative answers to several questions that have been circulating for some time. In particular, we show that the tensor product [math] between the bilinear Hilbert transform [math] and a paraproduct [math] satisfies the same [math] estimates as the [math] itself, solving completely a problem introduced by Muscalu et al. (Acta Math.…

  PublisherOA PDFDOI

• Quasi-Banach valued inequalities via the helicoidal method

  Journal of Functional Analysis · 2017-05-04 · 39 citations

  articleSenior author
  PublisherDOI

• Sparse domination via the helicoidal method

  arXiv (Cornell University) · 2017-07-18 · 17 citations

  preprintOpen accessSenior author

  51 pages

  PublisherOA PDF

• Sparse domination via the helicoidal method

  Revista Matemática Iberoamericana · 2021 · 14 citations

  Senior authorCorresponding

  Using exclusively the localized estimates upon which the helicoidal method was built by the authors, we show how sparse estimates can also be obtained. This approach yields a sparse domination for scalar and multiple vector-valued extensions of operators alike. We illustrate these ideas for an n -linear Fourier multiplier whose symbol is singular along a k -dimensional subspace of \Gamma=\{\xi_1+\cdots+\xi_{n+1}=0\} , where k < (n+1)/{2} , and for the variational Carleson operator.

  PublisherDOI

• Calderón commutators and the Cauchy integral on Lipschitz curves revisited II. The Cauchy integral and its generalizations

  Revista Matemática Iberoamericana · 2014-08-27 · 10 citations

  articleOpen access1st authorCorresponding

  This article is the second in a series of three papers, whose aim is to give new proofs to the well known theorems of Calderón, Coifman, McIntosh and Meyer [1], [4], and [5]. Here we treat the case of the Cauchy integral on Lipschitz curves and some of its generalizations.

  PublisherOA PDFDOI

Recent grants

• Topics in Multi-linear Harmonic Analysis

  NSF · $180k · 2007–2011

• Iterated Fourier Series and Integrals

  NSF · $240k · 2015–2019

Frequent coauthors

• Christoph Thiele

  49 shared

• Terence Tao

  University of California, Los Angeles

  48 shared

• Cristina Benea

  28 shared

• Wilhelm Schlag

  Yale University

  27 shared

• Jill Pipher

  19 shared

• Itamar Oliveira

  University of Birmingham

  7 shared

• Yen Do

  University of Virginia

  4 shared

• Yujia Zhai

  3 shared

Similar researchers at Cornell University

• Steven Strogatzh-89
• Daniel Sternh-58
• Anil Nerodeh-40