David Beltran

I am a Postdoctoral researcher at the Basque Center for Applied Mathematics (BCAM) in Bilbao.

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" bcamath.org;  
   (or)   dbeltran89 "at" gmail.com 

Web: http://www.bcamath.org/en/people/dbeltran
          http://web.mat.bham.ac.uk/dbeltran (outdated, no longer valid)

Address: Alameda de Mazarredo 14 
48009 Bilbao, Bizkaia 
(Basque-Country, Spain)

Telephone: +34 946 567 842

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 the regularity of classical maximal functions and in the geometric aspects of oscillatory Fourier multipliers, pseudodifferential operators and Fourier integral operators.

Publications and preprints

  • Sparse bounds for pseudodifferential operators, (with L. Cladek), submitted, arXiv
  • Control of pseudodifferential operators by maximal functions via weighted inequalities, to appear in Trans. Amer. 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, to appear in Rev. Mat. Iber., arXiv

Selected talks

  • Weighted inequalities for pseudodifferential operators, Congreso Bienial de la Real Sociedad Matematica Española, Zaragoza, Spain. 30 January 2017. (invited speaker for Harmonic Analysis session) slides
  • Weighted inequalities for oscillatory integrals, 10th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, Spain. 15 June 2016. (selected short talk) slides
  • Optimal weighted inequalities for the Carleson operator, Frontiers of Singular Integrals, Helsinki, Finland. 2 June 2015. (selected short talk) slides