Itamar Oliveira

I'm a research fellow in Analysis at the University of Birmingham (UK). My research interests are (broadly) in linear and multilinear harmonic analysis, as well as their applications to dispersive PDEs and connections to other areas, such as fractal geometry and combinatorics.

Research

Publicly available:

Mizohata-Takeuchi inequalities for orthonormal systems, with J. Bennett, N. Bez, S. Gutierrez and S. Nakamura, preprint 2025, 30 pages.
The oscillatory biest operator, joint with C. Benea, preprint 2024, 22 pages.
Probabilistic well-posedness of generalized cubic nonlinear Schrödinger equations with strong dispersion using higher order expansions, joint with J.-B. Casteras, J. Földes and G. Uraltsev, preprint 2024, 37 pages.
A phase-space approach to weighted Fourier extension inequalities, joint with J. Bennett, S. Gutiérrez and S. Nakamura, Forum of Mathematics, Sigma, 54 pages.
A new proof of Strichartz estimates for the Schrödinger equation in 2+1 dimensions, joint with C. Muscalu, From Classical Analysis to Analysis on Fractals - The Robert Strichartz Memorial Volume (2023), 24 pages.
A new approach to the Fourier extension problem for the paraboloid, joint with C. Muscalu, Analysis & PDE, Vol. 17 (2024), No. 8, 2841-2921, 81 pages.

Notes

Notes on the Kakeya maximal conjecture and related problems.
Notes on bilinear restriction.
Notes on Bourgain's Besicovitch type maximal operators and applications to Fourier analysis, written with Ben Foster and Alex Ortiz.

Travel/Events

Upcoming:

(Invited speaker) Harmonic Analysis and its Interactions @ Nagoya 2026 (Japan), February 16-20.
Instituto Superior Técnico, Lisbon (Portugal), December 8-11.

Past:

Basque Center for Applied Mathematics (Bilbao, Spain), August 28 - September 2, 2022.
University of Edinburgh (UK), October 9-12, 2022.
CIRM (Marseille, France) - Workshop Analyse réelle et géométrie, June 12-16, 2023.
Portorož (Slovenia) - Conference Contemporary Analysis and Its Applications, June 19-23, 2023.
Bilbao (Spain) - Harmonic Analysis and Differential Equations: new questions and challenges, September 5-8, 2023.
XI AGAPI day, ICMAT (Madrid, Spain), September 25-29, 2023.
Université de Nantes (France), October 21-28, 2023.
University of Loughborough (UK), November 8, 2023.
LMS Harmonic Analysis & PDE network meeting (Edinburgh, Scotland), December 3-4, 2023.
BCAM (Bilbao, Spain), March 11-15, 2024.
LMS Midlands Regional Meeting and Workshop (Loughborough, UK), April 2-4, 2024.
Cornell University (Ithaca, US), May 3-7, 2024.
University of Arkansas (Fayetteville, US), May 8-11.
Madison Lectures in Harmonic Analysis (Madison, US), May 13-17, 2024.
CIRM (Marseille, France) - Analyse harmonique et équations aux dérivées partielles, 10-14 June, 2024.
ICMAT (Madrid, Spain), 15-22 June, 2024.
Hausdorff Center for Mathematics (Bonn, Germany), July 8-19, 2024.
35th IWOTA (Canterbury, UK), August 12-16, 2024.
Quantum Signal Processing and Nonlinear Fourier Analysis (Oberwolfach, Germany), October 6-11, 2024.
Universitat Politècnica de Catalunya (Barcelona, Spain), November 28-29, 2024.
LMS Harmonic Analysis & PDE network meeting - UCC (Cork, Ireland), May 1st, 2025.
Universidade de Lisboa (Portugal), May 21-24.
Modern Trends in Fourier Analysis - CRM (Barcelona, Spain) - May 26th - June 6th, 2025.
El Escorial (Madrid, Spain) - June 9-13, 2025.
Brazilian Math Colloquium - IMPA (Rio de Janeiro, Brazil), July 27th - August 1st, 2025.
University of Edinburgh (UK), September 15, 2025.
LMS Harmonic Analysis & PDE network meeting, Birmingham (UK), October 22, 2025.
2nd Atlantic Conference in Nonlinear PDEs, Lisbon (Portugal), November 3-7, 2025.

Teaching

I will teach the second part of Advanced Topics in Analysis at UoB in the Spring of 2026.

Miscellaneous

A letter from Elias Stein to Bob Strichartz (1967), around the time when the Fourier restriction problem was posed. This was recovered from Bob's office in Cornell.
Birds and frogs, by Freeman Dyson.

Contacts:

lastname (dot) firstname (dot) w (at) gmail (dot) com

i.oliveira@bham.ac.uk

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