David Beltran
I am a Van Vleck Visiting Assistant Professor at the University of WisconsinMadison within the Analysis group. I am coorganising the Analysis seminar this Fall.
Contact details
Email: dbeltran "at" math "dot" wisc "dot" edu;
(or) dbeltran89 "at" gmail "dot" com
Address: Department of Mathematics University of WisconsinMadison 480 Lincoln Drive Madison, WI 53706, USA Office: 625 Van Vleck Hall
Phone: +1 (608) 2634700
Teaching Spring 2021:
 MATH 521, Section 001  Analysis I; MWF: 9.55am10.45am, (online). Course webpage: Canvas
 MATH 629  Introduction to Measure and Integration, MWF: 12.05pm12.55pm, (online). Course webpage: Canvas
 Fall 2020:
 MATH 421, Section 005  The Theory of Single Variable Calculus; MWF 5.40pm6.30pm, (online). Course webpage: Canvas
 Spring 2020:
 MATH 521, Section 001  Analysis I; MWF: 9.55am10.45am, SOC SCI 6102. Course webpage: Canvas
 MATH 521, Section 002  Analysis I; MWF: 12.05pm12.55pm, VV B119. Course webpage: Canvas
 Fall 2019:
 MATH 627  Introduction to Fourier Analysis; MWF 1.20pm2.10pm, 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. GonzálezRiquelme, 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
 Multiscale 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 kplane 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 Wolfftype 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 FeffermanStein inequality for the Carleson operator, Rev. Mat. Iberoam., arXiv

