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Gonçalves, Felipe
No

Felipe Ferreira Goncalves

Assistant Professor
Department of Mathematics



goncalves@utexas.edu


Office Location
PMA 11.124

Ph.D., IMPA - Brazil (2016)

Research Interests


I am mainly interested on questions in the interface of analysis and number theory, such as:
⬡ Packings, Uncertainty, Interpolation, Lattices and Modular forms
⬡ Sharp Inequalities in Analysis and Number Theory
⬡ Bandlimited Approximations, Sampling and Frames
⬡ Orthogonal Polynomials and Special Functions
⬡ Numerical Optimisation Applied to Number Theory (LP/SDP)
⬡ Quasiconformal maps

Published/Accepted Papers

  1. F. Gonçalves, David de Laat, and Nando Leijenhorst. Multiplicity of Non-trivial Zeros of Primitive L-functions via Higher-level Correlations. Mathematics of Computation (to appear).
  2. Henry Cohn, Dingding Dong and F. Gonçalves. Sign uncertainty principles and low-degree polynomials. Proceedings of the American Mathematical Society Series B 11(21):224-228.
  3. V. Ciccone and F. Gonçalves, Sharp Fourier Extension on the Circle Under Arithmetic Constraints. Journal of Functional Analysis 286, Issue 2, 15 January 2024, 110219.
  4. F. Gonçalves, Diogo Oliveira e Silva and João P. G. Ramos. New Sign Uncertainty Principles. Discrete Analysis 2023:9, 46 pp..
  5. F. Gonçalves, R. Greenfeld and J. Madrid. Generalized Collatz Maps with Almost Bounded Orbits. (Indiana University Mathematics Journal, to appear.
  6. F. Gonçalves and Don Zagier. Strichartz Estimates with Broken Symmetries. Rev. Mat. Iberoam. 38 (2022), no. 5, pp. 1709-1722.
  7. F. Gonçalves and João P. G. Ramos. A note on discrete Heisenberg uniqueness pairs for the parabola. Bulletin des Sciences Matématiques Volume 174, February 2022, 103095.
  8. F. Gonçalves and João P. G. Ramos. Bounds for the Lonely Runner Problem via Linear Programming. Bull Braz Math Soc, New Series (2022) 53:595–603.
  9. Andrés Chirre and F. Gonçalves. Bounding the log-derivative of the zeta-function. Mathematische Zeitschrift 300, pages 1041-1053 (2022).
  10. F. Gonçalves and Friedrich Littmann. Mean Convergence of Entire Interpolations in Weighted Space. Complex Analysis and Operator Theory 15:90 (2021).
  11. F. Gonçalves and Giuseppe Negro. Local maximizers of adjoint Fourier restriction estimates for the cone, paraboloid and sphere. Anal. PDE 15(4): 1097-1130 (2022).
  12. F. Gonçalves, Diogo Oliveira e Silva and João Ramos. On regularity and mass concentration phenomena for the sign uncertainty principle. The Journal of Geometric Analysis 31 (2021), 6080-6101.
  13. Andrés Chirre, F. Gonçalves and David de Laat. Pair Correlation Estimates for the Zeros of the Zeta-Function via Semidefinite Programming. Adv. in Math. 361, 12 February 2020, 106926.
  14. Henry Cohn and F. Gonçalves. An Optimal Uncertainty Principle in Twelve Dimensions via Modular Forms. Inventiones Mathematicae 217 (2019), Issue 3, pp 799-831. 
  15. F. Gonçalves, Diogo Oliveira e Silva and Stefan Steinerberger. A Universality Law for Sign Correlations of Eigenfunctions of Differential Operators. To appear in Journal of Spectral Theory.
  16. F. Gonçalves. A Sharpened Strichartz Inequality For Radial Functions. Journal of Functional Analysis, Volume 276, Issue 6, 15 March 2019, Pages 1925-1947.
  17. F. Gonçalves and Friedrich Littmann. Interpolation Formulas with Derivatives in De Branges Spaces II. J. Math. Anal. Appl., Volume 458, Issue 2, 15 February 2018, Pages 1091-1114.
  18. F. Gonçalves. Orthogonal Polynomials and Sharp Estimates for the Schrödinger Equation. International Mathematics Research Notices, Volume 2019, Issue 8, April 2019, Pages 2356-2383.
  19. F. Gonçalves. A Note on Band-limited Minorants of an Euclidean Ball. Proceedings of AMS, Volume 146, Number 5, May 2018, Pages 2063-2068.
  20. F. Gonçalves. An Uncertainty Principle for Roots. CMS Notes, Vol. 40, no.4, September 2017.                  
  21. F. Gonçalves, Diogo Oliveira e Silva and Stefan Steinerberger. Hermite Polynomials, Linear Flows on the Torus, and an Uncertainty Principle for Roots. J. Math. Anal. Appl. 451 (2017), issue 2, p. 678-711.
  22. F. Gonçalves.Interpolation formulas with derivatives in de Branges Spaces. Trans. Amer. Math. Soc. 369 (2017), 805-832.
  23. F. Gonçalves. A Central Limit Theorem for Operators. Journal of Functional Analysis, v. 271 (6), p. 1585-1603, (2016).
  24. Emanuel Carneiro and F. Gonçalves. Extremal problems in de Branges spaces: the case of truncated and odd functions. Mathematische Zeitschrift, v. 280, p. 17-45, (2015).
  25. F. Gonçalves, Michael Kelly and José Madrid. One-sided Band-limited Approximations of Some Radial Functions. Bulletin of Brazilian Mathematical Society, v. 46, no. 4, pp. 563-599 (2015).

Preprints

  1. José Afonso Barrionuevo, F. Gonçalves, José Victor Medeiros, Lucas Oliveira, On the Uniqueness of the Norton-Sullivan Quasiconformal extension.
  2. F. Gonçalves, A Classification of Fourier Summation Formulas and Crystalline Measures.
  3. F. Gonçalves, Daniel Keren, Amit Shahar, Gal Yehuda. Geometric Covering using Random Fields.
  4. F. Gonçalves and Guilherme Vedana. Sphere Packings in Euclidean Space with Forbidden Distances.
  5. Jacob Carruth, Noam D. Elkies, F. Gonçalves and Michael Kelly. The Beurling-Selberg Box Minorant Problem via Linear Programming Bounds.

 

 

The Office of Naval Research GRANT14201749 (award N629092412126).

Serrapilheira Grant Award : Serra-2211-41824

CAPES Award for Best Ph.D. Thesis in Mathematics of 2016.
Supported by CAPES and the Brazilian Ministry of Education.

Gutierrez Prize for Best Brazilian Ph.D. Thesis in Mathematics of 2016.
Supported by ICMC – São Carlos, University of São Paulo and the Brazilian Mathematical Society.

Analysis

Calculus of Variations

Differential Equations, Ordinary and Partial

Functional Analysis

Number Theory