Research

Submitted articles

27. Comparison theorems on H-type sub-Riemannian manifolds (with F. Baudoin, E. Grong, G. Molino) - [Preprint]

Published or accepted articles

26. Unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian structures (with D. Barilari, A. Mondino) - Mem. Amer. Math. Soc. (to appear) [Preprint]

25. Relative heat content asymptotics for sub-Riemannian manifolds (with A. Agrachev, T. Rossi) - Anal. PDE (to appear) - [Preprint]

24. Failure of curvature-dimension conditions on sub-Riemannian manifolds via tangent isometries (with G. Stefani) - J. Funct. Anal. 285 (2023), no. 9, Paper No. 110099 -[PDF]

23. Weyl's law for singular Riemannian manifolds (with Y. Chitour and D. Prandi) - J. Math. Pures Appl. 181 (2024), 113-151 - [PDF]

22. H-type foliations (with F. Baudoin, E. Grong, G. Molino) - Differ. Geom. Appl. 85 (2022) - [PDF]

21. Heat content asymptotics for sub-Riemannian manifolds (with T. Rossi) - J. Math. Pures Appl. 148 (2021), 267-307 - [PDF]

20. Branching geodesics in sub-Riemannian geometry (with T. Mietton) - Geom. Funct. Anal. 30 (2020), 1139–1151 - [PDF]

19. Bakry-Émery curvature and model spaces in sub-Riemannian geometry (with D. Barilari) - Math. Ann. 377 (2020), no. 1-2, 435--482 - [PDF]

18. On the essential self-adjointness of singular sub-Laplacians (with V. Franceschi and D. Prandi) - Potential Anal. 53 (2020), no. 1, 89--112 - [PDF]

17. Sub-Riemannian interpolation inequalities (with D. Barilari) - Invent. Math. 215 (2019), no. 3, 977--1038  - [PDF - ADDENDUM]

16. A counterexample to gluing theorems for MCP metric measure spaces - Bull. Lond. Math. Soc. 50 (2018), no. 5, 781--790 - [PDF]

15. Sharp measure contraction property for generalized H-type Carnot groups (with D. Barilari) - Commun. Contemp. Math. 20 (2018), no. 6, 1750081, 24 pp. - [PDF] 

14. Quantum confinement on non-complete Riemannian manifolds (with D. Prandi and M. Seri) - J. Spectr. Theory 8 (2018), no. 4, 1221--1280 - [PDF]

13. A sub-Riemannian Santaló formula with applications to isoperimetric inequalities and first Dirichlet eigenvalue of hypoelliptic operators (with D. Prandi and M. Seri) - J. Differential Geom. 111 (2019), no. 2, 339--379. - [PDF]

12. Sub-Riemannian Ricci curvatures and universal diameter bounds for 3-Sasakian manifolds (with P. Silveira) - J. Inst. Math. Jussieu 18 (2019), no. 4, 783--827 - [PDF]

11. Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling (with A. Agrachev, U. Boscain and R. Neel) - ESAIM Control Optim. Calc. Var. 24 (2018), no. 3, 1075--1105 -  [PDF]

10. Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry (with U. Boscain and R. Neel) - Adv. Math. 314 (2017), 124--184 - [PDF]

9. On Jacobi fields and a canonical connection in sub-Riemannian geometry (with D. Barilari) - Arch. Math. (Brno) 53 (2017), no. 2, 77--92 - [PDF]

8. On the cut locus of free, step two Carnot groups (with U. Serres) - Proc. Amer. Math. Soc. 145 (2017), no. 12, 5341--5357 - [PDF]

7. Measure contraction properties of Carnot groups - Calc. Var. Partial Differential Equations 55 (2016), no. 3, Art. 60, 20 pp - [PDF]

6. Sub-Riemannian curvature in contact geometry (with A. Agrachev and D. Barilari) - J. Geom. Anal. 27 (2017), no. 1, 366--408 - [PDF]

5. A formula for Popp's volume in sub-Riemannian geometry (with D. Barilari) - Anal. Geom. Metr. Spaces 1 (2013), 42--57 - [PDF]

4. On conjugate times of LQ optimal control problems (with A. Agrachev and P. Silveira) - J. Dyn. Control Syst. 21 (2015), no. 4, 625--641 - [PDF]

3. Comparison theorems for conjugate points in sub-Riemannian geometry (with D. Barilari) - ESAIM Control Optim. Calc. Var. 22 (2016), no. 2, 439--472 - [PDF]

2. How many geodesics join two points on a contact sub-Riemannian manifold? (with A. Lerario) - J. Symplectic Geom. 15 (2017), no. 1, 247--305 - [PDF]

1. Curvature: a variational approach (with A. Agrachev and D. Barilari) - Mem. Amer. Math. Soc. 256 (2018), no. 1225, v+142 pp. - [PDF]

Proceedings

2. An introduction to Sub-Laplacians and their self-adjointness properties - in Mini-Workshop: Self-adjoint Extensions in New Settings. Oberwolfach Rep. 16 (2020), no. 4, 2911--2950

1. Recent results on the essential self-adjointness of sub-Laplacians, with some remarks on the presence of characteristic points (with V. Franceschi and D. Prandi) - Séminaire de Théorie spectrale et géométrie (Grenoble), 33 (2015-2016), p. 1-15

Habilitation à diriger des recherches (HDR)

Interpolation inequalities and spectral geometry on sub-Riemannian structures - Institut Fourier (Grenoble), 8 juillet 2021

Published articles (Physics*)

*In the years 2009/10, during my undergraduate studies, I've been active in the field of analogue gravity in collaboration with Profs. F. Belgiorno, S. Cacciatori, D. Faccio and V. Gorini and in other projects with Profs. O. Piattella, V. Gorini et al. In fall 2010 I started a PhD program in mathematics, under the supervision of Prof. A. Agrachev. For this reason my scientific production includes papers in physics (published in 2010-2011) and mathematics (2012 onward).

Some Slides & Talks**

**no longer constantly updated