Research
I am fascinated by problems in number theory and arithmetic geometry. My primary interests are Euler systems, Iwasawa theory, and some aspects of the theory of automorphic representations. I have recently been working on instances of conjectures of Beilinson and Tate for symplectic Shimura varieties and on cases of the Birch and Swinnerton-Dyer conjecture for elliptic curves over totally real fields.
This is a month-long documentary of the 713 corridor blackboard at UCL and it was submitted by my colleague, friend, and artist James Cann to the UCL Research Images as Art exhibition in 2019. I am proud to see that, without knowing, some fun calculations of mine on flag varieties were turned into beautiful art.
In preparation
Kato's theorem for elliptic curves over totally real number fields, joint work with D. Barrera, S. Molina, and V. Rotger.
Preprints
A two variable Rankin-Selberg integral for GU(2,2) and the degree 5 L-function of GSp(4), joint work with A. Gutierrez Terradillos (arXiv).
Spherical Shalika models on GU(2,2) and the theta correspondence for (GSp(4),GU(2,2)), joint work with A. Gutierrez Terradillos (arXiv).
Tempered currents and Deligne cohomology of Shimura varieties, with an application to GSp(6), joint work with J. I. Burgos Gil, F. Lemma, and J. Rodrigues Jacinto (arXiv).
On higher regulators of Siegel varieties, joint work with F. Lemma and J. Rodrigues Jacinto (arXiv).
Publications
Algebraic cycles and functorial lifts from G2 to PGSp(6), joint work with F. Lemma and J. Rodrigues Jacinto, to appear in Algebra & Number Theory (arXiv).
On analogues of Mazur-Tate type conjectures in the Rankin-Selberg setting, joint work with A. Lei, Publicacions Matemàtiques, 66, pp. 571-630, 2022 (journal), (arXiv).
Norm-compatible systems of Galois cohomology classes for GSp(6), joint work with J. Rodrigues Jacinto, Documenta Mathematica, 25, pp. 911-954, 2020 (journal), (arXiv).
Norm-compatible systems of cohomology classes for GU(2, 2), International Journal of Number Theory, 16 (3), pp. 461-510, 2020 (journal), (arXiv).
Other writings
On classes in the motivic cohomology of certain Shimura varieties, PhD thesis (link).