Ricardo Menares


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Publications

6) (with José Burgos Gil and Juan Rivera-Letelier) On the essential minimum of Faltings' height. Math. Comp. 87 (2018), no. 313, 2425–2459. arXiv:1609.00071

5) (with Nicolas Billerey) Strong modularity of reducible Galois representations. Trans. Amer. Math. Soc. 370 (2018), no. 2, 967–986. arXiv:1604.01173

4) (with Nicolas Billerey) On the modularity of reducible mod l Galois representations. Math. Res. Lett. 23 (2016), no. 1, 15–41. arXiv:1309.3717

3) (with Florian Luca and Amalia Pizarro-Madariaga) On shifted primes with large prime factors and their products. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 1, 39–47. arXiv:1311.2527

2) Equidistribution of Hecke points on the supersingular module. Proc. Amer. Math. Soc. 140 (2012), no. 8, 2687–2691. arXiv:1303.1320

1) Correspondences in Arakelov geometry and applications to the case of Hecke operators on modular curves.  Manuscripta Math. 136 (2011), no. 3-4, 501–543 arxiv: 0911.0546

0) Ph. D. Thesis: Nombres d'intersection arithmétiques et opérateurs de Hecke sur les courbes modulaires. tel-00360171



Other mathematical texts

(with José Burgos Gil) Equidistribución, teoría del potencial y aplicaciones aritméticas. Notes for a course in AGRA III school. v1, July 2018.
We cover elementary concepts from potential theory and apply them to prove the classical Fekete-Szegö theorem, including a slight refinement showing equidistribution in the case of capacity one. We also cover Bilu's theorem on equidistribution of points with small height in tori. These notes are mostly self-contained.

Construcciones geométricas sólo con compás, Revista del profesor de Matemáticas, Año 8, número 1.

Tate Algebras (2011)
These notes are a compilation of facts and proofs about Tate algebras.




Grants

april 2017-march 2021 : Fondecyt Regular 1171329 (PI)
2017-2019 : ECOS-CONICYT (member)
2016: PEPS, CNRS (member, PI: Nicolas Billerey)
2015-2016 : Proyectos internos PUCV 24.750/2015, 124.756/2016 (PI)
2014 : MEC 80130064, CONICYT (sponsor)
2012-2014: Proyecto interno PUCV 124.734/2012 (PI)
2011-2014 : Fondecyt Iniciación 11110225 (PI)