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 Differential Geometry (Riemannian and sub-Riemannian manifolds), contact structures, jet bundles, models of the Visual Cortex, elliptic PDEs

This is my complete Curriculum Vitæ

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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.

Critical singular problems in Carnot groups. arXiv
Under review.
Joint work with Stefano Biagi and Eugenio Vecchi.

An extension to non-nilpotent groups of Rothschild-Stein lifting method. arXiv
Under review.

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

October 2025 UPCOMING - Presenting a talk 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 at Università di 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

July 2023 - I co-organized the conference Sub-Riemannian Geometry Harmonic Analysis, PDEs and Applications at Università di Bologna

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

May 2021 - Between virtuality and formal gesture: thinking about the rare event
Talk presented jointly with Luca Cabassa at the seminar of Post-structural dynamics (online), EHESS, Paris

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

Events NEW

June 2025 - Three Days in Sub-Riemannian Geometry, Università di Bologna.

June 2024 - Noncommutativity at the Interface of Topology, Geometry and Analysis, Università di Bologna.

Teaching

For the a.a. 2025/2026 I am teaching professor for the course 28622 - ANALISI MATEMATICA TA at Energy Engeneering. Here you can find some notes for the course (in italian), they're also available on the website of Maria Gaetana Agnesi project.

For the a.a. 2024/2025 I am teaching professor for the course 87295 - ANALISI MATEMATICA TA at Energy Engeneering. Here you can find various online resources and a section for official notices.

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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