Mattia Galeotti

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

Here my page on the

You can also find my profile on

NEWS

↣ In June 2026, I will organize NONPub 26 with Simone Ciani, at the University of Bologna

My math publications

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
Joint work with Stefano Biagi and Eugenio Vecchi.
Accepted for publication on The Journal of Geometric Analysis.

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

July 2026 - UPCOMING I am presenting the talk Critical problems in Carnot groups at the 15th AIMS Conference in Athens.

June 2026 - UPCOMING I am co-organizing 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.

Ocotber 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

June 2026 Upcoming - NONPub 26, University of Bologna. Organized with Simone Ciani.

June 2025 - Three Days in Sub-Riemannian Geometry, University of Bologna. Organizing Committee.

June 2024 - Noncommutativity at the Interface of Topology, Geometry and Analysis, University of Bologna. Organizing Committee.

July 2023 - Sub-Riemannian Geometry Harmonic Analysis, PDEs and Applications, University of Bologna. Organizing Committee.

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

I contributed to the anthology Epistemologie, critiche e punti di fuga nel dibattito contemporaneo (in italian).
I translated, with Luca Cabassa, the texts of Gilles Châtelet, Ismael - Van Fraassen, Longo - Montévil.

Discrimination and algorithms. Encounters and confrontations between different definitions of fairness (in italian). journal
Published on The Lab’s Quarterly, 2018, XX, 4.

My PhD thesis.

Other stuff

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