David Beltran

I am a Van Vleck Visiting Assistant Professor at the University of Wisconsin-Madison within the Analysis group.

Previously, I was a postdoctoral researcher at the Basque Center for Applied Mathematics (BCAM) in Bilbao (Bilbao Analysis and PDE).

I received a P.h.D from the University of Birmingham in Summer 2017 under the supervision of Jonathan Bennett, being a member of the Analysis group.

Here is my CV and a copy of my PhD thesis.

Contact details

Email: dbeltran "at" math "dot" wisc "dot" edu;  
   (or)   dbeltran89 "at" gmail "dot" com 

Address: Department of Mathematics
University of Wisconsin-Madison
480 Lincoln Drive
Madison, WI 53706, USA
Office: 625 Van Vleck Hall

Phone: +1 (608) 263-4700


Teaching
  • Fall 2019: MATH 627 - Introduction to Fourier Analysis

Research interests

My main research interests lie in the area of Euclidean harmonic analysis and its interactions with dispersive PDE, geometric measure theory and analytic number theory. Particular examples are questions related to the Fourier restriction conjecture, decoupling inequalities, local smoothing estimates, maximal Radon transforms, the Kakeya conjecture and extremisers for Strichartz estimates. I am also interested in the recent developments on sparse operators that have led to optimal results in classical weighted harmonic analysis, in questions related to the regularity of classical maximal functions and in the geometric aspects of oscillatory Fourier multipliers, pseudodifferential operators and Fourier integral operators.

Publications and preprints

  • The circular maximal function for Heisenberg radial functions, (with S. Guo, J. Hickman and A. Seeger), in preparation.
  • Bilinear identities involving the k-plane transform and Fourier extension operators, (with L. Vega), submitted, arXiv
  • Endpoint Sobolev continuity of the fractional maximal function in higher dimensions, (with J. Madrid), submitted, arXiv
  • Regularity of fractional maximal functions through Fourier multipliers, (with J.P. Ramos and O. Saari), J. Funct. Anal., arXiv
  • Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds, (with J. Hickman and C. D. Sogge), to appear in Anal. PDEarXiv
  • Sparse bounds for pseudodifferential operators, (with L. Cladek), to appear in J. Anal. Math., arXiv
  • Control of pseudodifferential operators by maximal functions via weighted inequalities, Trans. Amer. Math. Soc., arXiv
  • Subdyadic square functions and applications to weighted harmonic analysis, (with J. Bennett), Adv. Math., arXiv
  • A Fefferman-Stein inequality for the Carleson operator, Rev. Mat. Iberoam., arXiv

Expository papers