João Pedro Ramos

RG Analysis and Partial Differential Equations

Contact

Postal address:	Office:
Mathematisches Institut	Endenicher Allee 60, N2.011
Universität Bonn	Phone: +49 (0) 228 73-2928
Endenicher Allee 60	E-mail: jpgramos (at) math.uni-bonn.de
D - 53115 Bonn

I am currently a PhD student under the supervision of Prof. Dr. Christoph Thiele.

My current CV. (last updated July 8th, 2019)

Preprints and Publications

F. Goncalves, D. Oliveira e Silva and J.P. Ramos On the equivalence of some root uncertainty principles. In preparation.
J. P. Ramos, M. Sousa Fourier Uniqueness pairs of powers of integers. Preprint .
J. P. Ramos, O. Saari and J. Weigt Weak differentiability for fractional maximal functions of general Lp functions on domains. Submitted .
J. P. Ramos The Hilbert transform along the parabola, the polynomial Carleson theorem, and oscillatory singular integrals. Submitted.
J.P. Ramos Low-dimensional maximal restriction principles for the Fourier transform. Submitted.
J.P. Ramos Maximal restriction estimates and maximal functions of the Fourier transform. Accepted to the Proceedings of the American Mathematical Society.
D. Beltran, J.P. Ramos and O. Saari Regularity of fractional maximal functions through Fourier multipliers. Accepted to the Journal of Functional Analysis.
J.P. Ramos Sharp total variation results for maximal functions. Accepted to the Annales Academiae Scientiarum Fenniciae.

My Master's degree was obtained in IMPA, Rio de Janeiro, Brazil, by February 29th, 2016. It was substituted, according to the institute's official rules, by two Ph.D. courses, one of which comprised a final written work, completed by me on the topic of: Time-Frequency Analysis and Carleson's Theorem: A Student's point of view. Advisor: Prof. Claudio Landim; Final work tutor: Prof. Emanuel Carneiro. This work is a detailed version of the work A proof of boundedness of the Carleson operator, by M. Lacey and C. Thiele.

My Bachelor's degree was obtained in UFRJ, Rio de Janeiro, Brazil, by March 31st, 2016, in applied mathematics. Its final work was substituted, according to the university's official rules, by the work above.Advisor: Prof. Emanuel Carneiro.

Research interests

My main area of interest is analysis in the broad sense, with a particular interest for harmonic analysis, geometric analysis and partial differential equations.

More specifically, my current research interests lie on the theory of regularity of maximal functions - as the first cited work emphasizes -, uncertainty principles and their relations to number theory and harmonic analysis, which has to do with the second project cited above, and time-frequency analysis and its applications, one area of interest shared with my current advisor, Prof. Christoph Thiele, one of the reasons why I did my master's final project on Carleson's theorem.