Vita                                                             photo gallery

Antonio Córdoba was born in 1949, graduated in Mathematics in 1971 (Universidad Complutense) and got his PhD in 1974 under the supervision of C. Fefferman (University of Chicago). Since 1980 he has had a Chair in Mathematics Analysis at Universidad Autónoma de Madrid. He has held visiting professor positions at several universities.

His research has ranged from number theory to mathematical physics, with his main interests being harmonic analysis and PDEs. Throughout his career he has shown a remarkable talent for teaching at all levels, from graduate courses to talks for the general public. He has authored a book on number theory, "Introduction to number theory" with J. Cilleruelo, and a textbook for freshmen about sets and numbers, "The numbers saga".

Prof. Córdoba has supervised nine doctoral theses: A. Ruiz (Inverse problems); B. López-Melero (Maximal functions, Bochner-Riesz summability); B. Barceló (Restriction of the Fourier transform to a conical surface); L. Vega (Schrödinger operators); J. Barceló (Band limited functions); J. Cilleruelo (Number Theory); F. Chamizo (Number Theory); P. Balodis (Quantum Mechanics: stability of matter); and P. Fernández-Gallardo (Fourier Analysis and Crystalography).

He manages, with J.L. Fernández, the Revista Matemática Iberoamericana, the leading Spanish mathematical journal.

We list some of his major research achievements:
The precise covering lemma satisfied by parallelepipeds in Rn
Córdoba, A.; Fefferman, R. A geometric proof of the strong maximal theorem. Ann. of Math. (2) 102 (1975), no. 1, 95-100.
Sharp estimates for the 2-dimensional Kakeya maximal function
Córdoba, A. The Kakeya maximal function and the spherical summation multipliers. Amer. J. Math. 99 (1977), no. 1, 1-22.
A wave packet theory of Fourier integral operators
Córdoba, A.; Fefferman, C. Wave packets and Fourier integral operators. Comm. Partial Differential Equations 3 (1978), no. 11, 979-1005.
Proof of a conjecture of A. Zygmund about differentiation bases
Córdoba, A: A proof of a conjecture of A. Zygmund, Bull. AMS, vol 1 (1) (1979), 255-257.
A geometric proof of Bochner-Riesz conjecture for dimension 2
Córdoba, A. A note on Bochner-Riesz operators. Duke Math. J. 46 (1979), no. 3, 505-511.
A proof of that Bragg's peaks  imply periodic structure
Cordoba, A. Dirac combs. Lett. Math. Phys. 17 (1989), no. 3, 191-196.
Lattice points in small arcs of a circle
Cilleruelo, J.; Cordoba, A. Trigonometric polynomials and lattice points. Proc. Amer. Math. Soc. 115 (1992), no. 4, 899-905.
A number-theoretical approach to the energy of large atoms
Córdoba, A.; Fefferman, C.L.; Seco, L.A. A number-theoretic estimate for the Thomas-Fermi density. Comm. Partial Differential Equations 21 (1996), no. 7-8, 1087--1102.
Fractal behaviour of Fourier series with polynomial frequencies
Chamizo, F.; Córdoba, A. Differentiability and dimension of some fractal Fourier series. Adv. Math. 142 (1999), no. 2, 335-354.
Blow-up in finite time for a one-dimensional model
Córdoba, A. Córdoba, D., Fontelos, M.A. Formation of singularities for a transport equation with nonlocal velocity. Ann. of Math. (2) 162 (2005), no. 3, 1377-1389.
On the conjecture of De Giorgi in dimension n>7
Caffarelli, L.A.; Córdoba, A. Phase transitions: Uniform regularity of the intermediate layers. Journal Reine Angew. Math., 593 (2006), 209-235.
The solution of the Muskat and Hele-Shaw problem for different densities and viscosities
Córdoba, A. Córdoba, D., Gancedo, F. Interface evolution: the Hele-Shaw and Muskat problems. In press.