Researcher

François Charles

François Charles is an algebraic geometer who advises AI companies on the responsible release of AI-generated mathematical results. He entered École normale supérieure in 2004, earned a mathematics doctorate under Claire Voisin in 2010, and worked at the CNRS and MIT before returning as a professor at Université Paris-Saclay. His research includes proving the Tate conjecture for K3 surfaces over finite fields of characteristic greater than 3 and an arithmetic Bertini theorem published in 2021. He directs ENS-PSL's Department of Mathematics and Applications and serves on the independent Advisory Group on Mathematics and Artificial Intelligence.

Timeline

  1. 2004–2010

    ENS and a mathematics doctorate

    After two years of preparatory classes, he enters École normale supérieure in 2004. He defends his doctorate in mathematics under Claire Voisin in 2010 while serving as an agrégé-préparateur at ENS.

  2. 2013

    The Tate conjecture for K3 surfaces

    In 2013, his paper proves Artin's conjecture for supersingular K3 surfaces over finite fields of characteristic greater than 3; this yields the Tate conjecture for K3 surfaces in that range.

  3. 2013–2014

    Cours Peccot at Orsay

    After his 2010 doctorate, the CNRS recruits him, and he spends several years at MIT before returning to France as a professor at Université Paris-Saclay's Laboratoire de Mathématiques d'Orsay. He receives the Cours Peccot for 2013–2014.

  4. 2021

    An arithmetic Bertini theorem

    In 2021, he publishes “Arithmetic ampleness and an arithmetic Bertini theorem.” The theorem shows that, on a projective arithmetic variety of dimension at least two, the proportion of effective sections defining an irreducible divisor tends to 1 as powers of an ample hermitian line bundle grow.

  5. June 2025

    Director of ENS's mathematics department

    In June 2025, he becomes director of ENS-PSL's Department of Mathematics and Applications, a joint research unit of ENS and CNRS.

  6. September–October 2026

    Co-founding an AI math advisory group

    In September 2026, he joins the Advisory Group on Mathematics and Artificial Intelligence as one of its nine members. The independent group advises AI companies on interactions with mathematical research and on responsible release of results. It publishes guidelines on September 29, 2026, and responds to OpenAI's release on October 6, 2026.

Sources and credits

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  1. François Charles | SFEIR sfeir.com. Checked 19 October 2026.
  2. The Tate conjecture for K3 surfaces over finite fields arxiv.org. Checked 19 October 2026.
  3. François Charles | Collège de France college-de-france.fr. Checked 19 October 2026.
  4. Arithmetic ampleness and an arithmetic Bertini theorem arxiv.org. Checked 19 October 2026.
  5. Advisory Group on Mathematics and Artificial Intelligence agmai.org. Checked 19 October 2026.