The MELODIA Project

Methods for low-dimensional abelian varieties

Members

Samuele Anni is an associate professor at Aix-Marseille University. His research focuses on Galois representations attached to arithmetic objects, with an emphasis on congruences of modular forms, study of structure of torsion of abelian varieties and local–global problems. He took part to the EPSRC Program Grant LMF: L-Functions and Modular Forms (2013–2016) and the DFG priority project SPP 1489 Computational aspects of modular forms and p-adic Galois representations (COMFGREP).

Gaetan Bisson is an associate professor at the University of French Polynesia since 2013. His expertise lies with effective aspects of abelian varieties and CM theory. He has obtained important results on the computation of endomorphism rings which this project will improve and generalize. He was previously awarded a Macquarie Research Development Grant and a STIC-AmSud Grant. Furthermore, he has been serving as the deputy director of the GAATI laboratory since 2019 and has organized four international conferences (including series such as GEOCRYPT and AGC2T).

Elisa Lorenzo García is an associate professor at the Université de Rennes 1. Her research is on effective aspects of projective curves and varieties. She recently won the Prize Julio Peláez to the Women Pioneers of Physics, Chemistry and Mathematics and has been named Woman Scientist of the month (09/19) of the European Platform for Women Scientists.

Alexander D. Rahm is a full professor at the University of French Polynesia. He has developed new techniques for working with modular forms and group cohomology. With 18 high profile publications in the 9 years since his PhD defense, he has been nominated for National University of Ireland's President's Award for Research Excellence. He has a widespread network of international collaborators and a substantial track record of project supervision, including 4 PhD theses.

Benjamin Wesolowski is a CNRS researcher at the University of Bordeaux. His research focuses on mathematical cryptanalysis, connecting cryptography to classical mathematical theories. He has obtained significant results on the discrete logarithm problem, the shortest vector problem in algebraic lattices, and the structure of certain isogeny graphs of ordinary abelian varieties. He was awarded the Best young researcher paper award at Eurocrypt 2019, the Doctoral Program Thesis Distinction 2019 at the EPFL and an Ethereum Foundation Grant in 2019.