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 732928 
Endenicher Allee 60  Email: jpgramos (at) math.unibonn.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 Lowdimensional 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: TimeFrequency 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 timefrequency 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.
Slides and Notes
 The Variation of the Centered Maximal Function (after O. Kurka)
 Formal proof of an useful inequality involving Hausdorff measures of level sets
Teaching
 Assistant Introduction to Nonlinear Dispersive Equations (Brazilian Summer 2016), Instituto de Matematica Pura e Aplicada (IMPA) (carried out in Portuguese).
 Course notes V4B5: Real and Harmonic Analysis (winter term 2016/2017)
 Tutor Modul math240 Mathematik II (Mathematics for Physicists II) (summer term 2018) (carried out in German).
 Tutor V2B1  Analysis III (winter term 2018/19) (carried out in German).
 Assistant V4B5  Real and Harmonic Analysis (summer term 2019).
 Organizer S5B1  Graduate seminar on Advanced topics in PDE (summer term 2019)
News
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Prof. Peter Scholze erhält Verdienstorden der Bundesrepublik Deutschland
Prof. Dr. Valentin Blomer wurde zum Mitglied der Academia Europaea gewählt
Prof. Peter Scholze erhält FieldsMedaille 2018