Gregorio Baldi

Chargé de Recherche, CNRS
Institut de Mathématiques de Jussieu - Paris Rive gauche

Bureau 15-25-436

My e-mail address is
my surname[at]imj-prg[dot]fr

I am chargé de recherche with the CNRS at IMJ-PRG.

Picture courtesy of Andrea Kane, Institute for Advanced Study.

Research

I work in Arithmetic Geometry and I am mainly interested in Shimura varieties, variational Hodge theory, the Zilber-Pink conjecture, homogeneous and Teichmüller dynamics.

Newest

Algebraic Hodge generic points are dense (with G.Binyamini and D.Urbanik) arXiv, 2026.
Automorphisms of the moduli space of smooth cubic surfaces and its fundamental group (with B.Farb, A.Javanpeykar, and M.Stover) arXiv, 2026.
Intersections and the Bézout Range: Abelian Varieties (with D.Urbanik), arXiv, 2026.

Geometry of the Hodge locus and applications

Effective atypical intersections and applications to orbit closures (with D.Urbanik), arXiv, 2024.
Rich representations and superrigidity, (with N.Miller, M.Stover, and E.Ullmo), arXiv, Ergodic Theory and Dynamical Systems (2025).
Non-density of the exceptional components of the Noether-Lefschetz locus, (with B.Klingler and E.Ullmo), arXiv, IMRN, Volume 2024, Issue 21 (2024), 13642–13650.
On the distribution of the Hodge locus, (with B.Klingler and E.Ullmo), arXiv, slides, Inventiones mathematicae, Volume 235, 441-487, (2024).
Special subvarieties of non-arithmetic ball quotients and Hodge Theory (with E.Ullmo), arXiv, slides, Ann. of Math, 159-220, Volume 197 (2023), (erratum).

Arithmetic aspects of Zilber-Pink

On the Geometric Ziber-Pink Theorem and the Lawrence-Venkatesh method, (with B.Klingler and E.Ullmo), arXiv, Expo. Math.41 (2023), no.3, 718-722 (Volume in honour of Bas Edixhoven).
Manin-Mumford in arithmetic pencils, (with R.Richard and E.Ullmo), arXiv, 2021.
On a conjecture of Buium and Poonen, arXiv, journal, slides. Annales de l'Institut Fourier, Tome 70 (2020) no. 2, pp. 457-477.

Rational points of Shimura varieties

Finite descent obstruction for Hilbert modular varieties (with G.Grossi), arXiv, journal, Canadian Math. Bull., Vol. 64-2 (2021), pp. 452 - 473.
Local to global principle for the moduli space of K3 surfaces, arXiv, journal, slides. Arch. Math. (2019) 112: 599.

Other papers

What makes an algebraic curve special?, arXiv, 2025.
Hodge theory and o-minimality at CIRM, arXiv, 2025.
On the geometric Mumford-Tate conjecture for subvarieties of Shimura varieties, arXiv, journal. Proc. Amer. Math. Soc. 148 (2020).
Some remarks on motivical and derived invariants, arXiv, 2019.

Theses and HDR

Lieu de Hodge et applications : quelques résultats et conjectures, HDR (Habilitation à diriger des recherches), slides (May 2025).
Shimura varieties, Galois representations and motives, PhD thesis (September 2020).