Optimal Transport: new challenges across Analysis and Geometry (n. 2022K53E57)
Type
PRIN 2022, D.D. n. 104 del 2 febbraio 2022
CUP
C53D2300250006
Principal Investigator
Fabio Cavalletto (Scuola Internazionale Superiore di Studi Avanzati di TRIESTE - SISSA) poi sostituito dal co-PI
Davide Barilari (Università degli Studi di Padova - Dipartimento di Matematica "Tullio Levi Civita")
Other research units
UO1 - Fabio CAVALLETTO poi sostituito dal 01/10/2023 da Antonio LERARIO - Scuola Internazionale Superiore di Studi Avanzati di TRIESTE - SISSA
UO2 - Davide BARILARI - Università degli Studi di PADOVA
Duration
28/09/2023 - 30/09/2025
Description
In recent years, Optimal Transport has been at the centre of major developments in mathematics at the frontier of analysis, probability, geometry and data science. The scope of our project is to address important open problems and questions across analysis and geometry adopting the pivotal new techniques coming from the Optimal Transport theory.
We outlined three main lines of research:
a) Localization paradigm in Optimal Transport
b) Optimal Transport theory between algebraic varieties
c) sub-Riemannian geometry and Optimal transport
Activities
CONFERENCE
Title: New challenges across Analysis and Geometry
Date: May 12–14, 2025
Location: SISSA, Trieste
Website: https://sites.google.com/view/new-challenges-across-analysis/home
Speakers
Eugenio Bellini (UNIPD)
Samuel Borza (Wien)
Tania Bossio (UNIPD)
Fabio Cavalletti (UNIMI)
Lorenzo Cecchi (SISSA)
Marco Di Marco (UNIPD)
Karen Habermann (Warwick)
Alessandro Tamai (SISSA)
Lucia Tessarolo (Sorbonne)
Matteo Testa (SISSA)
Daniele Tiberio (UNIPD)
Related publications
[1] D. Barilari, T. Bossio, V. Franceschi, Magnetic fields on sub-Riemannian manifolds ArXiv Preprint (Apr 2025)
[2] V. Franceschi, R. Monti, and A. Socionovo, Mean value formulas on surfaces in Grushin spaces. Annales Fennici Mathematici, 49(1), 241–255, 2024
[3] V. Franceschi, A. Pinamonti, G. Saracco, G. Stefani, The Cheeger problem in abstract measure spaces. accepted on J. London Math. Society 109, 2024: e12840
[4] A. Lerario, L. Rizzi and D. Tiberio, Sard properties for polynomial maps in infinite dimension, preprint arXiv:2407.02296
[5] A. Lerario, P. Bürgisser, P. Breiding and L. Mathis, Probabilistic intersection theory in Riemannian homogeneous spaces, preprint arXiv:2502.08256
[6] A. Lerario, L. Rizzi and D. Tiberio, Quantitative approximate definable choices, Math. Ann., to appear.
[7] A. Lerario, P. Roos Hoefgeest, M. Scolamiero and A. Tamai, Testing the variety hypothesis, preprint arXiv:2507.16705
[8] Tania Bossio, Luca Rizzi, Tommaso Rossi - Tubes in sub-Riemannian geometry and a Weyl's invariance result for curves in the Heisenberg groups - preprint arXiv:2408.16838
[9] Andrei A. Agrachev, Stefano Baranzini, Eugenio Bellini, Luca Rizzi - Quantitative tightness for three-dimensional contact manifolds: a sub-Riemannian approach, accepted on Nonlinearity.
[10] Giovanni Russo, Andrew Swann, Nearly parallel G_2-structures with torus symmetry, arXiv:2508.21703.
[11] Giovanni Russo, Topics in representation theory and Riemannian geometry, arXiv:2504.13689.
[12] Anna Fino, Gueo Grantcharov, and Giovanni Russo, On the \nu-invariant of two-step nilmanifolds with closed G_2-structure, arXiv:2409.06870.
[13] D. Barilari, E. Bellini, A. Pinamonti, Curvature measures and the sub-Riemannian Gauss-Bonnet theorem.
Arxiv Preprint (Oct 2025), 33 pages.
[14] D. Barilari, S. Flynn, Refined Strichartz estimates for sub-Laplacians in Heisenberg and H-type groups, ArXiv Preprint (Jan 2025), 32 pages.
