Suprematism in Harmonic Analysis

Antonio Córdoba obtained his doctoral degree from the University of Chicago in 1974 under the guidance of mathematician and Fields Medalist Charles Fefferman. Currently holding the position of Mathematics Analysis Professor at the Universidad Autónoma de Madrid, he has served as the director of the Institute of Mathematical Sciences (ICMAT-CSIC) since 2016. During his tenure at Princeton University, he published a paper in the "Annals of Mathematics" that solved the Zygmund conjecture, a problem that had persisted for over 50 years, marking one of his significant contributions to mathematics. His research work spans over foundational contributions in areas such as Fourier analysis, mathematical physics, differential equations, fluid dynamics and number theory, with publications in top international journals including the "Annals of Mathematics", "Inventiones Mathematicae", and "Communications on Pure and Applied Mathematics". He founded the "Ibero-American Journal of Mathematics". In 2011, he was awarded the "Julio Rey Pastor" National Research Prize in Mathematics and Information and Communication Technologies. A member of the Royal Spanish Mathematical Society, he has served as the chairman of its scientific committee, is an honorary member of the Murcia Region Academy of Sciences, a member of the Free Honorary University, and an honorary doctor of the University of Murcia. He serves as a technical advisor on scientific committees, participates in the advisory committee of the President's Higher Council for Scientific Research, and works for national physics and mathematics evaluation agencies.

Preface.- Notions and terminology.- 1. Seven mathematical haikus.- 2. All those rectangles.- 3. As a needle turn: Besicovitch or Kakeya sets.- 4. Translation invariant operators.- 5. The multiplier problem for the ball.- 6. The ball multiplier on mixed norm spaces.- 7. The Poisson summation formula.- 8. Encounters at the interface with number theory.- 9. Weyl sums and atomic energy oscillations.- Bibliography.