My Education Manifesto

I have been thinking about math education for more than fifteen years. An initiation rite for me was the following story. I was training three students for the math olympics in some school. They worked with me for one year without previous trainment. Then they went to the National Mathematical Olympiad in Chile and they obtained the three gold medals that were given that year. In that moment I was very moved and I realized that the method that I implemented (a method that has been evolving ever since) was interesting.

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Entrevista en radio Pauta

Fui entrevistado por la muy motivada y entretenida Maritxu Sangroniz en el programa "Un día perfecto" de la radio Pauta.…

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Pre-canonical bases on affine Hecke algebras

Joint with Leo Patimo and David Plaza. Submitted to Advances in Mathematics.  For any affine Weyl group, we introduce the pre-canonical bases, a set of bases of the spherical Hecke algebra that interpolates between the standard basis and the canonical basis. Thus we divide the hard problem of calculating Kazhdan-Lusztig polynomials (or q-analogues of weight multiplicities) into a finite number of much easier problems.

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p-Jones Wenzl idempotent

Joint work with Gastón Burrull and Paolo Sentinelli. . Advances in Mathematics  352 (2019) 246-264. In this paper we introduce the p-Jones Wenzl idempotent, a characteristic p analogue of the classical Jones-Wenzl idempotent. We hope this to be a building block for the p-canonical basis as sl_2 is a building block for the representation theory of semi-simple Lie algebras.

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Revista Héurèka

Artículo en la primera edición de la revista héurèka, dedicada a la divulgación  de la ciencia.

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Blob algebra approach to modular representation theory

Joint work with David Plaza. Proc. Lond. Math. Soc. Vol. 121 (2020) Issue3, 656-701. We conjecture (and prove the "graded degree part") an equivalence between the type A affine Hecke category in positive characteristic and a certain blob category that we introduce as a quotient of KLR algebras. This conjecture has been proved recently in an amazing paper by Chris Bowman, Anton Cox, Amit Hazi!! It opens lots of questions...

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