Research

Research interests

Harmonic Analysis and Analytic Number Theory.

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 Papers

• Sharp endpoint extension inequalities for the moment curve on finite fields

(with C. Biswas, T. Flock, D. Oliveira e Silva, B. Stovall and J. Tautges) 

Preprint.

• Effective equidistribution of Galois orbits for mildly regular test functions

(with M. K. Das) 

Preprint.

• Sharp embeddings between weighted Paley-Wiener spaces

(with C. González-Riquelme, L. Oliveira, A. Olivo, S. Ombrosi, A. P. Ramos and M. Sousa)

Preprint.

• Fourier optimization, the least quadratic non-residue, and the least prime in an arithmetic progression

(with M. Milinovich, E. Quesada-Herrera and A. P. Ramos)

to appear in Mathematics of Computation.

• On sharp Fourier extension from spheres in arbitrary dimensions

(with G. Negro and D. Oliveira e Silva) 

to appear in Harmonic Analysis and Nonlinear Partial Differential Equations, RIMS Kôkyûroku Bessatsu (Lecture notes from RIMS - Kyoto).

• Sign uncertainty and de Branges spaces

(with T. Ismoilov and A. P. Ramos)

to appear in Annales de l'Institut Fourier (Grenoble).

• Fourier optimization and Montgomery's pair correlation conjecture

(with M. Milinovich and A. P. Ramos)

Mathematics of Computation, vol. 94 (2025), no. 351, 409-424.

• Stability of sharp Fourier restriction to spheres 

(with G. Negro and D. Oliveira e Silva) 

Journal of Fourier Analysis and Applications  30 (2024), no. 6, Paper No. 70.

• On Littlewood's estimate for the modulus of the zeta function on the critical line 

(with M. Milinovich)

Proceedings of the International Conference Constructive Theory of Functions, Lozenets (2023), pp. 1-16, BAS, Sofia, 2024.

• Monotone extremal functions and the weighted Hilbert's inequality

(with F. Littmann) 

Portugaliae Mathematica, vol. 81 (2024), no. 1-2, 127-134. 

• Generalized sign Fourier uncertainty 

(with E. Quesada-Herrera)

Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, vol. 24 (2023), 1671-1704.

• Sunrise strategy for the continuity of maximal operators 

(with C. González-Riquelme and J. Madrid)

Journal d'Analyse Mathématique, vol. 148 (2022), no. 1, 37-84.

• Hilbert spaces and low-lying zeros of L-functions 

(with A. Chirre and M. Milinovich)

Advances in Mathematics, vol. 410 (2022), Paper No. 108748 (48 pages).  

• Optimality for the two-parameter quadratic sieve 

(with A. Chirre, H. Helfgott and J. Mejia-Cordero)

Acta Arithmetica, vol. 203 (2022), no. 3, 195-226.

• On Montgomery's pair correlation conjecture: a tale of three integrals 

(with V. Chandee, A. Chirre and M. Milinovich)

Journal für die reine un angewandte Mathematik (Crelle's journal), vol. 786 (2022), 205-243.

• Gaussians never extremize Strichartz inequalities for hyperbolic paraboloids 

(with L. Oliveira and M. Sousa)

Proceedings of the American Mathematical Society, vol. 150 (2022), no. 8, 3395-3403. 

• Hilbert transforms and the equidistribution of zeros of polynomials 

(with M. K. Das, A. Florea, A. Kumchev, A. Malik, M. Milinovich, C. Turnage-Butterbaugh and J. Wang - an AIM Workshop project) 

Journal of Functional Analysis, vol. 281 (2021), no. 9, 109199.

• Gradient bounds for radial maximal functions 

(with C. González-Riquelme)

 Annales Fennici Mathematici, vol. 46 (2021), 495-521.

• Extremizers for adjoint Fourier restriction on hyperboloids: the higher dimensional case 

(with D. Oliveira e Silva, M. Sousa and B. Stovall)

Indiana University Mathematics Journal, vol. 70 (2021), 535-559.

• Bounds for zeta and primes via Fourier analysis

Extended Abstracts Fall 2019 - spaces of analytic functions: approximation, interpolation, sampling, 59-64. Trends in Mathematics. Research Perspectives CRM Barcelona. Birkhäuser/Springer, Cham. 2021 

• Sharp mixed norm spherical restriction 

(with D. Oliveira e Silva and M. Sousa) 

Advances in Mathematics, vol. 341 (2019), 583-608.

• Fourier optimization and prime gaps 

(with M. Milinovich and K. Soundararajan) 

Commentarii Mathematici Helvetici, vol. 94 (2019), no. 3, 533-568.

• Bandlimited approximations and estimates for the Riemann zeta-function 

(with A. Chirre and M. Milinovich)

Publicacions Matemàtiques, vol. 63 (2019), no. 2, 601-661.

• Extremizers for Fourier restriction on hyperboloids 

(with D. Oliveira e Silva and M. Sousa)

Annales de l'Institut Henri Poincaré Analyse Non Linéaire, vol. 36 (2019), no. 2, 389-415.

• Regularity of maximal operators: recent progress and some open problems 

Applied and Numerical Harmonic Analysis - New Trends in Harmonic Analysis, vol. 2 (2019), Chapter 3, 69-92. Birkhäuser, Cham. 

• Bounding $S_n(t)$ on the Riemann hypothesis 

(with A. Chirre)

Mathematical Proceedings of the Cambridge Philosophical Society, vol. 164 (2018), 259-283.

• On the variation of maximal operators of convolution type II 

(with R. Finder and M. Sousa)

Revista Matemática Iberoamericana, vol. 34 (2018), 739-766.

• Endpoint Sobolev and BV continuity for maximal operators 

(with J. Madrid and L. B. Pierce)

Journal of Functional Analysis, vol. 273 (2017), 3262-3294.

• Derivative bounds for fractional maximal functions 

(with J. Madrid)

Transactions of the American Mathematical Society, vol. 369 (2017), 4063-4092.

• Hilbert spaces and the pair correlation of zeros of the Riemann zeta-function 

(with V. Chandee, F. Littmann and M. Milinovich)

Journal für die reine und angewandte Mathematik (Crelle's journal), vol. 725 (2017), 143-182.

• A sharp trilinear inequality related to Fourier restriction on the circle 

(with D. Foschi, D. Oliveira e Silva and C. Thiele)

Revista Matemática Iberoamericana, vol. 33 (2017), 1463-1486.

• Extremal functions in de Branges and Euclidean spaces II 

(with F. Littmann)

American Journal of Mathematics, vol. 139 (2017), 525-566.

• A note on the zeros of zeta and L-functions 

(with V. Chandee and M. Milinovich)

Mathematische Zeitschrift, vol. 281 (2015), 315-332.

• On the argument of L-functions 

(with R. Finder)

Bulletin of the Brazilian Mathematical Society, vol. 46, no. 4 (2015), 601-620.

• Some sharp restriction inequalities on the sphere 

(with D. Oliveira e Silva)

International Mathematics Research Notices (IMRN), vol. 2015 (2015), 8233-8267.

• Extremal problems in de Branges spaces: the case of truncated and odd functions 

(with F. Gonçalves)

Mathematische Zeitschrift, vol. 280 (2015), 17-45.

• Extremal functions in de Branges and Euclidean spaces 

(with F. Littmann)

Advances in Mathematics, vol. 260 (2014), 281-349.

• On the variation of maximal operators of convolution type 

(with B. Svaiter)

Journal of Functional Analysis, vol. 265 (2013), 837-865.

• Entire approximations for a class of truncated and odd functions 

(with F. Littmann)

Journal of Fourier Analysis and Applications, vol. 19 (2013), 967-996.

• Bounding $S(t)$ and $S_1(t)$ on the Riemann hypothesis 

(with V. Chandee and M. Milinovich)

Mathematischen Annalen, vol. 356, no. 3 (2013), 939-968.

• Bandlimited approximations to the truncated Gaussian and applications 

(with F. Littmann)

Constructive Approximation, vol. 38, no. 1 (2013), 19-57.

• Gaussian subordination for the Beurling-Selberg extremal problem 

(with F. Littmann and J. D. Vaaler)

Transactions of the American Mathematical Society, vol. 365 (2013), 3493-3534.

• On the endpoint regularity of discrete maximal operators 

(with K. Hughes)

Mathematical Research Letters, vol. 19, no. 6 (2012), 1245-1262.

• On a discrete version of Tanaka's theorem for maximal functions 

(with J. Bober, K. Hughes and L. B. Pierce)

Proceedings of the American Mathematical Society, vol. 140 (2012), 1669-1680.

• A survey on Beurling-Selberg majorants and some consequences of the Riemann hypothesis

Matemática Contemporânea 40 (2011), 149–172. 

• Bounding $\zeta(s)$ in the critical strip 

(with V. Chandee)

Journal of Number Theory, vol. 131 (2011), 363-384.

• Convolution inequalities for the Boltzmann collision operator 

(with R. J. Alonso and I. M. Gamba)

Communications in Mathematical Physics, vol. 298, no. 2 (2010), 293-322.

• Estimates for the Boltzmann collision operator via radial symmetry and Fourier transform 

(with R. Alonso)

Advances in Mathematics, vol. 233, no. 2 (2010), 511-528.

• Some extremal functions in Fourier analysis III 

(with J. D. Vaaler)

Constructive Approximation, vol. 31, no. 2 (2010), 259-288.

• Some extremal functions in Fourier analysis II 

(with J. D. Vaaler)

Transactions of the American Mathematical Society, vol. 362 (2010), 5803-5843.

• A sharp inequality for the Strichartz norm

International Mathematical Research Notices IMRN 16 (2009), 3127-3145. 

• Sharp approximations to the Bernoulli periodic functions by trigonometric polynomials

Journal of Approximation Theory, vol. 154 (2008), 90-104.

• On the regularity of maximal operators 

(with D. Moreira)

Proceedings of the American Mathematical Society, vol. 136 (2008), 4395-4404. 

Ph.D. students

1. Tolibjon Ismoilov, SISSA, current.

2. Antonio Pedro Ramos, SISSA, 2025.

Thesis: Fourier optimization, de Branges spaces, and zeros of L-functions.

3. Emily Quesada-Herrera, IMPA, 2022.

Thesis: On uncertainty principles, Fourier optimization and the Riemann zeta-function.

Carlos Gutierrez Thesis Prize 2023 (video).

4. Cristian González-Riquelme, IMPA, 2021.

Thesis: Fine properties of maximal operators.

5. Andrés Chirre, IMPA, 2020. (video of the defense)

Thesis: Bounds for the Riemann zeta-function via Fourier analysis. 

IMPA Thesis Prize 2020, CAPES Thesis Prize 2020, Carlos Gutierrez Thesis Prize 2020 (video).

6. Mateus Sousa, IMPA, 2017. 

Thesis: Some sharp inequalities in harmonic analysis.

7. Renan Finder, IMPA, 2016. 

Thesis: Variation-diminishing maximal operators and the argument of L-functions.

8. José Madrid, IMPA, 2016. 

Thesis: Regularity of fractional maximal functions and extremal functions of exponential type.

9. Felipe Gonçalves, IMPA, 2016. 

Thesis: Extremal problems, reconstruction formulas and approximations of Gaussian kernels.

IMPA Thesis Prize 2017, CAPES Thesis Prize 2017, Carlos Gutierrez Thesis Prize 2017.

M.Sc. students

1. Gabriele Nani, M.Sc. UNITS, 2024. 

2. Muhammad Atif Zaheer, M.Sc. LUMS - Pakistan, 2024.

3. Tainara Borges, M.Sc. IMPA, 2020.

4. Cynthia Bortolotto, M.Sc. IMPA, 2020.

5. Alvaro Gomez, M.Sc. IMPA, 2017.

6. Gerardo Paredes,  M.Sc. IMPA, 2017.

7. Itamar Oliveira, M.Sc. Univ. Federal do Ceará (co-advised with D. Moreira), 2016.

8. Renan Finder, M.Sc. IMPA, 2012.

ICTP Postgraduate Diploma students

1. Emmanuel Obongi, ICTP, 2023.

2. Abraham Orinda, ICTP, 2023.

3. Laurence Wijaya, ICTP, 2022.

4. Tolibjon Ismoilov, ICTP, 2022.

5. Rahama Sani, ICTP, 2021.

6. Khakimboy Egamberganov, ICTP, 2019.

7. Carlos Ospina, ICTP, 2019.