David Beltran
I am a Ramón y Cajal Research Fellow (named Tenure Track Assistant Professor) at the Universitat de València since August 2022.
From 2019-2022, I was a Van Vleck Assistant Professor at the University of Wisconsin-Madison within the Analysis group. From 2017-2019, 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 June 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.
Email: david "dot" beltran "at" uv "dot" es; (or) dbeltran89 "at" gmail "dot" com
Address: Departament d'Anàlisi Matemàtica
Universitat de València
Dr Moliner 50
46100 Burjassot (València), Spain
Office: 313 Edifici Jeroni Muñoz Phone: +34 (9635) 44525
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, Bochner--Riesz means, radial Fourier multipliers, 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
Localised variants of multilinear restriction, (with J. Duncan and J. Hickman), submitted, arXiv
Bochner--Riesz means at the critical index: weighted and sparse bounds, (with J. Roos and A. Seeger), submitted, arXiv
Off-diagonal estimates for the helical maximal function, (with J. Duncan and J. Hickman), Proc. Lond. Math. Soc., arXiv
On sharp isoperimetric inequalities on the hypercube, (with P. Ivanisvili and J. Madrid), submitted, arXiv
Endpoint sparse domination for classes of multiplier transformations, (with J. Roos and A. Seeger), Math. Z. , arXiv
L^p-L^q local smoothing estimates for the wave equation via k-broad Fourier restriction, (with O. Saari), J. Fourier Anal. Appl., arXiv
Continuity of the gradient of the fractional maximal operator in W^{1,1}(R^d), (with C. González-Riquelme, J. Madrid and J. Weigt), Math. Res. Lett., arXiv.
Sobolev improving for averages over curves in R^4, (with S. Guo, J. Hickman and A. Seeger), Adv. Math., arXiv
Sharp L^p bounds for the helical maximal function, (with S. Guo, J. Hickman and A. Seeger), to appear in Am. J. Math. , arXiv
Variation bounds for spherical averages, (with R. Oberlin, L. Roncal, A. Seeger and B. Stovall), Math. Annalen, arXiv
Multi-scale sparse domination, (with J. Roos and A. Seeger), to appear in Mem. Amer. Math. Soc., arXiv.
The circular maximal operator on Heisenberg radial functions, (with S. Guo, J. Hickman and A. Seeger), 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. IMRN, 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), Anal. PDE, arXiv
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
A note on endpoint Bochner--Riesz estimates, (with J. Roos and A. Seeger), Oberwolfach Preprint, also available here
Sharp local smoothing estimates for Fourier integral operators, (with J. Hickman and C. D. Sogge), conference proceedings of 'Geometric Aspects of Harmonic Analysis', Springer INdAM series 45, Chapter 2, on the occasion of Fulvio Ricci's 70th birthday, arXiv
Teaching
A la Universitat de València
Spring 2024 (2n quadrimestre):
Anàlisi Harmònica, Grau en Matemàtiques; Dilluns-Dimecres 17.00-19.00, aula 0.5 (Facultat de Matemàtiques, Bloc G). Fitxa de l'assignatura Página de la asignatura: Aula Virtual o aquí
Fall 2023 (1r quadrimestre):
Fundamentos de matemática avanzada (Teoria de la medida), Máster Universitario en Investigación Matemática; Martes-Jueves 15.30-17.45, aula 1.5 (Facultat de Matemàtiques, Bloc G). Fitxa de l'assignatura
Spring 2022 (2n quadrimestre):
Matemàtiques II, Grau en Enginyeria Electrònica de Telecomunicacions; aula AE 2.1.7 E.T.S.E. Calendari
Fall 2022 (1r quadrimestre):
Matemàtiques I, Grup C, Grau en Química; Teoria. 1pm-2pm a l'aula F1.1 (Facultat de Química, Bloc F) els dies que apareixen al calendari. Per a seminaris i pràctiques d'informatica, consulteu ací en funció del vostre grup. Enllaços a Aula Virtual, Guía Docent i Dates Exàmens
At UW-Madison
Spring 2022:
Fall 2021:
Spring 2021:
Fall 2020:
Spring 2020:
Fall 2019:
MATH 627 - Introduction to Fourier Analysis; MWF 1.20pm-2.10pm, VV B231. Course webpage: Canvas or here