Blowup illustration

Là où calculer est impossible, suggérer s'impose
M. Bloch


Mattia Galeotti



I am a post-doc (Ricercatore di Tipo A) in Mathematics at Università di Bologna
I obtained my PhD at the IMJ, Sorbonne Université, Paris

Email: mattia(dot)galeotti4(at)unibo(dot)it
Address: Dipartimento di Matematica, Piazza di Porta San Donato 5 - 40126 Bologna
My office is number I3 at the I level (5th floor, on the north side of the building)

My research topics are sub-Riemannian geometry and contact geometry, elliptic and sub-elliptic PDEs, optimal transport, models of the visual cortex and deformation theory.

This is my complete Curriculum Vitæ cv

Here my page on the    arxiv

You can also find my profile on
orcid researchgate google scholar scopus



NEWS

↣ In September 2026, I will give a talk at the Ask Conference 2026, in Bologna.



My math publications
  • The weak Harnack inequality and the rigidity of the anisotropic Trudinger's equation. arXiv
     Under review.
     Joint work with Simone Ciani and Igor Skrypnik.

  • Benamou-Brenier and Kantorovich on sub-Riemannian manifolds with no abnormal geodesics. arXiv
     Under review.
     Joint work with Giovanna Citti and Andrea Pinamonti.

  • An extension to non-nilpotent groups of Rothschild-Stein lifting method. arXiv
     Accepted for publication on Publicacions Matemàtiques.

  • Critical singular problems in Carnot groups. arXiv, journal
     Joint work with Stefano Biagi and Eugenio Vecchi.
     Published on J. Geom. Anal. 36, 268(2026).

  • Critical concave-convex problems in Carnot groups. arXiv, journal
     Joint work with Eugenio Vecchi.
     Published on Nonlinear Differ. Equ. Appl. 33, 77 (2026).

  • A heterogeneous model of boundary and figure completion in V1. journal
     Joint work with Giovanna Citti and Alessandro Sarti.
     Published on Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2025. Lecture Notes in Computer Science, vol 16035. Springer, Cham.

  • The cortical V1 transform as a heterogeneous Poisson problem. arXiv, journal
     Joint work with Alessandro Sarti and Giovanna Citti.
     Published on SIAM Journal on Imaging Sciences 17 (1) (2024).

  • Differential Operators Heterogenous in Orientation and Scale in the Cortext. journal
     Joint work with Giovanna Citti and Alessandro Sarti.
     Published on Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, vol 14072, pp.465-473.

  • Cortically based optimal transport. arXiv, journal
     Joint work with Giovanna Citti and Alessandro Sarti.
     Published on Journal of Mathematical Imaging and Vision (2022).

  • Birational geometry of moduli of curves with an S3-cover. arXiv, journal

     Published on Advances in Mathematics. Vol. 389, 2021.

  • Moduli of G-covers of curves: geometry and singularities. arXiv, journal

     Published on Annales de l'Institut Fourier 72 (6), 2022.

  • Moduli spaces of abstract and embedded Kummer varieties. arXiv, journal
     Joint work with Sara Perna.
     Published on International Journal of Mathematics. Vol. 32, No. 08, 2150054 (2021).

  • Singularities of moduli of curves with a universal root. arXiv, journal

     Published on Documenta Mathematica n.22 (2017).
Talks and other
  • September 2026 - UPCOMING I am presenting a talk at the Ask Conference 2026.

  • July 2026 - Critical problems in Carnot groups (slides).
    Talk presented at the 15th AIMS Conference, Athens, in the Special Session "Recent advances in local and nonlocal PDEs".

  • June 2026 - I co-organized the conference NONPub 26 with Simone Ciani, at the University of Bologna.

  • October 2025 - A heterogeneous model of boundary and figure completion in V1.
    Talk presented at GSI'25, Geometric Science of Information in St. Malo, France.

  • October 2025 - The Benamou-Brenier formulation of optimal transport on sub-Riemannian manifolds.
    Talk presented at the Differential Equation Seminar of the University Roma Tor Vergata.

  • September 2025 - Benamou-Brenier and Kantorovich are equivalent on sub-Riemannian manifolds with no abnormal geodesics.
    Talk presented at Workshop on Geometric Variational Problems in Sub-Riemannian Geometry, Universidad de Granada.

  • June 2025 - A Sub-Riemannian version of the Benamou-Brenier Theorem.
    Poster presented at Sub-Riemannian Geometry and Beyond, IV in Fribourg, Switzerland.

  • October 2024 - A lifting and saturation method for non-nilpotent lie groups.
    Talk presented at the Periodic Seminar of the Mathematics Department in Trento.

  • March 2024 - Global fundamental solutions for Hörmander operators via a saturation method.
    Talk presented at Pini Seminar, University of Bologna.

  • February 2024 - The visual V1 cortex action as a heterogeneous differential operator.
    Poster presented at the Bio-PDE Days 2024 in Vienna, Austria

  • September 2023 - Differential operators heterogeneous in orientation and scale in the V1 cortex.
    Talk presented at the conference GSI'23, Geometric Science of Information in St. Malo, France

  • February 2023 - Poisson’s equation with heterogeneous differential operators
    Poster presented at the "Mathematics and Image Analysis, MIA conference 2023" that took place at Humboldt Universitat, Berlin, and at the "VISAPP 2023, 18th International Conference on Computer Vision Theory and Application" that took place in Lisbon

  • April 2021 - Birational geometry and singularities of moduli of curves with a spin bundle or a principal bundle
    Talk presented at the conference "Days of algebraic geometry and correlated subjects XV" (online), Università di Milano

  • April 2018 - Singularities and global geometry of moduli of curves with spin and principal bundles
    Talk presented at the Pure Mathematics Seminar of the University of Liverpool

  • October 2017 - Moduli of curves with principal and spin bundles: singularities and global geometry
    Talk presented at the Geometry Seminar of the University of Pisa

  • May 2017 - Curves with a root bundle and their ghost automorphisms
    Talk presented at the seminar of young researchers in geometry, University of Rennes 1

  • April 2015 - On the singularities of R_{g,ell}^k
    Talk presented at IMPA, Rio de Janeiro
Events
Teaching
  • For the a.a. 2026/2027 I am teaching professor for the course 28622 - ANALISI MATEMATICA TA at the faculty of Energy Engeneering, as I was in 2025/2026 and in 2024/2025. Here you can find some notes for the course (in italian).

  • In Janaury and February 2026 I taught the PhD course Sub-Riemannian geodesics

  • For the a.a. 2023/2024 I was teaching professor for the course 66877 - ANALISI MATEMATICA at Informatics. Here you can find various online resources and a section for official notices.

  • In 2020 and 2021 I was teaching assistant and teaching professor at Università di Bologna for graduate courses in basic mathematics and analysis at the faculties of economics, engineering and informatics.

  • From 2014 to 2017 I was teaching assistant at Université Pierre et Marie Curie for undergraduate courses in basic mathematics, linear algebra and probability.
Other publications
Other stuff
  • Micelio is a newsletter (in italian) that focus on the role of sciences and techniques in our world

  • eXtemporanea is a beautiful community of scientists and non-scientists that you may be interested in following