My research lies at the interface of number theory and algebraic geometry. I am particularly interested in

[1] (with J. Fernández de Bobadilla, V. Muñoz, and A. Murillo) The Hilali conjecture for hyperelliptic spaces

[2] Periods of Hodge structures and special values of the gamma function

[3] (with O. Amini, S. Bloch, and J.I. Burgos Gil) Feynman amplitudes and limits of heights

Video of a lecture by Spencer Bloch about this work.

[4] A reciprocity law for periods of cyclic covers

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

[6] (with P. Jossen) Exponential motives

Videos of lectures at MSRI, Luminy and HIM.

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

[8] (with C. Sabbah and J-D. Yu) Hodge theory of Kloosterman connections

Video of a lecture at Luminy.

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

[10] (with C. Sabbah and J-D. Yu) Quadratic relations between Bessel moments

[11] (with P. Jossen) A non-hypergeometric E-function

[12] (with W. Sawin, A. Forey, and E. Kowalski) Quantitative sheaf theory

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

[1] (with J. I. Burgos Gil) Multiple zeta values: from numbers to motives

[2] Équirépartition de sommes exponentielles (travaux de Katz)

Video of the lecture.

[3] Une introduction aux périodes

Videos of lecture 1 and lecture 2.

[4] Hodge theory and o-minimality (after B. Bakker, Y. Brunebarbe, B. Klingler, and J. Tsimerman)

Video of the lecture.

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