David Beltran

I am a Van Vleck Visiting Assistant Professor at the University of Wisconsin-Madison within the Analysis groupI am co-organising the Analysis seminar this Fall.

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
  • Spring 2021:
    • MATH 521, Section 001 - Analysis I; MWF: 9.55am-10.45am, (online). Course webpage: Canvas
    • MATH 629 - Introduction to Measure and Integration, MWF: 12.05pm-12.55pm, (online). Course webpage: Canvas
  • Fall 2020:
    • MATH 421, Section 005 - The Theory of Single Variable Calculus; MWF 5.40pm-6.30pm, (online). Course webpage: Canvas
  • Spring 2020
    • MATH 521, Section 001 - Analysis I; MWF: 9.55am-10.45am, SOC SCI 6102. Course webpage: Canvas  
    • MATH 521, Section 002 - Analysis I; MWF: 12.05pm-12.55pm, VV B119. Course webpage: Canvas 
  • Fall 2019
    • MATH 627 - Introduction to Fourier Analysis; MWF 1.20pm-2.10pm, VV B231. Course webpage: Canvas

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, averages along manifolds, maximal and variation norm 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

  • Continuity of the gradient of the fractional maximal operator in W^{1,1}(R^d), (with C. González-Riquelme, J. Madrid and J. Weigt), submitted, arXiv.
  • Sobolev improving for averages over curves in R^4, (with S. Guo, J. Hickman and A. Seeger), submitted, arXiv 
  • Sharp L^p bounds for the helical maximal function, (with S. Guo, J. Hickman and A. Seeger), submitted, arXiv
  • Variation bounds for spherical averages, (with R. Oberlin, L. Roncal, A. Seeger and B. Stovall), submitted, arXiv
  • Multi-scale sparse domination, (with J. Roos and A. Seeger), submitted, arXiv.
  • The circular maximal operator on Heisenberg radial functions, (with S. Guo, J. Hickman and A. Seeger), to appear in Ann. Sc. Norm. Super. Pisa Cl. Sci., arXiv.
  • Regularity of the centered fractional maximal function on radial functions, (with J. Madrid), J. Funct. Anal., arXiv
  • Bilinear identities involving the k-plane transform and Fourier extension operators, (with L. Vega), Proc. A Royal Soc. Edinburgh, arXiv
  • Endpoint Sobolev continuity of the fractional maximal function in higher dimensions, (with J. Madrid), Int. Math. Res. Not. IMRNarXiv
  • 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), Anal. PDEarXiv
  • Sparse bounds for pseudodifferential operators, (with L. Cladek), 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