Publications


My research lies at the interface of number theory and algebraic geometry. I am particularly interested in periods, a class of complex numbers which appear when comparing de Rham and Betti cohomology of algebraic varieties over number fields.


Research papers

[1] (with J. Fernández de Bobadilla, V. Muñoz, and A. Murillo) The Hilali conjecture for hyperelliptic spaces
Mathematics without boundaries: Surveys in Pure Mathematics (P. Pardalos and Th. M. Rassias, eds.), Springer-Verlag, 2014, 21-36.

[2] Periods of Hodge structures and special values of the gamma function
Inventiones mathematicae 208 (2017), no. 1, 247-282.

[3] (with O. Amini, S. Bloch, and J.I. Burgos Gil) Feynman amplitudes and limits of heights
Izvestiya: Mathematics 80 (2016), no. 5, special volume in honor of J-P. Serre, 813-848.
Video of a lecture by Spencer Bloch about this work.

[4] A reciprocity law for periods of cyclic covers
In preparation.

[5] (with M. Asakura) On the Gross-Deligne conjecture for variations of Hodge-de Rham structures
Preprint.

[6] (with P. Jossen) Exponential motives
Preliminary version.
Videos of lectures at MSRI, Luminy and HIM.

[7] (with P. Jossen) Algebraic cogroups and Nori motives
Submitted.

[8] (with C. Sabbah and J-D. Yu) Hodge theory of Kloosterman connections
Duke Mathematical Journal, accepted.
Video of a lecture at Luminy.

[9] (with C. Sabbah and J-D. Yu) Quadratic relations between periods of connections
Tohoku Mathematical Journal, accepted.

[10] (with C. Sabbah and J-D. Yu) Quadratic relations between Bessel moments
Algebra & Number Theory, accepted.

[11] (with P. Jossen) A non-hypergeometric E-function
Annals of Mathematics 194 (2021), no. 3, 903-942.

[12] (with W. Sawin, A. Forey, and E. Kowalski) Quantitative sheaf theory
Journal of the American Mathematical Society, accepted.

[13] (with A. Forey, and E. Kowalski) Arithmetic Fourier transforms over finite fields: generic vanishing, convolution, and equidistribution
Submitted.


Surveys

[1] (with J. I. Burgos Gil) Multiple zeta values: from numbers to motives
Clay Mathematics Proceedings, to appear.

[2] Équirépartition de sommes exponentielles (travaux de Katz)
Séminaire Bourbaki, 70ème année, 2017-2018, no. 1141, Astérisque 414 (2019), 205-250
Video of the lecture.

[3] Une introduction aux périodes
Périodes et transcendance, Éditions de l'École polytechnique, 2021.
Videos of lecture 1 and lecture 2.

[4] Hodge theory and o-minimality (after B. Bakker, Y. Brunebarbe, B. Klingler, and J. Tsimerman)
Séminaire Bourbaki, 72ème année, 2019-2020, no. 1170, Astérisque 430 (2021), 131-157
Video of the lecture.


Books edited

[1] (with D. Jetchev, P. Jossen and R. Pink) Motives and Complex Multiplication
Progress in Mathematics, in preparation.