Ph.D obtained in 2003 at Universitat de Barcelona under the supervision of prof. Pilar Bayer. Associate professor at UPC since 2005; full professor since 2018. Long research stays at Tata Institute of Fundamental Research (Bombay), McGill University (Montréal), Humboldt University (Berlin), Aristotle University (Salonika). ERC Consolidator Grant 2016-2022.

Research interests

In 2000, the Clay Mathematics Institute established seven Prize Problems, conceived to record some of the most important problems with which mathematicians were grappling at the turn of the second millennium. One of these problems is the conjecture of Birch and Swinnerton-Dyer (BSD) on the arithmetic of elliptic curves. My research is devoted to this question and generalizations of it within the scenario provided by the Langlands program, due to Stark for Artin representations and to Beilinson, Bloch and Kato for arbitrary motives.

I have been working on proving new cases of the BSD Conjecture (posed in 1965), the Bloch-Kato conjecture (1990), Darmon’s conjecture on Stark-Heegner points (1999), the elliptic Stark conjecture (2015), Venkatesh’s conjecture (2018) among other outstanding problems. I have also built new research directions on  Euler systems and the p-adic Kudla program.

Keywords

Shimura varieties, Birch and Swinnerton-Dyer conjecture, Elliptic curves, L-functions, Motivic Cohomology