## Published

1. Curvature: a variational approach (with A. Agrachev and D. Barilari) -

2. How many geodesics join two points on a contact sub-Riemannian manifold? (with A. Lerario) -

3. Comparison theorems for conjugate points in sub-Riemannian geometry (with D. Barilari) -

4. On conjugate times of LQ optimal control problems (with A. Agrachev and P. Silveira) -

5. A formula for Popp's volume in sub-Riemannian geometry (with D. Barilari) -

6. Sub-Riemannian curvature in contact geometry (with A. Agrachev and D. Barilari) -

7. Measure contraction properties of Carnot groups -

8. On the cut locus of free, step two Carnot groups (with U. Serres) - Proceedings of the AMS - [PDF]

9. On Jacobi fields and a canonical connection in sub-Riemannian geometry (with D. Barilari) -

10. Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry (with U. Boscain and R. Neel) -

11. Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling (with A. Agrachev, U. Boscain and R. Neel) -

12. Sub-Riemannian Ricci curvatures and universal diameter bounds for 3-Sasakian manifolds (with P. Silveira) -

13. A sub-Riemannian Santaló formula with applications to isoperimetric inequalities and first Dirichlet eigenvalue of hypoelliptic operators (with D. Prandi and M. Seri) -

14. Quantum confinement on non-complete Riemannian manifolds (with D. Prandi and M. Seri) - Journal of Spectral Theory (in press) - [PDF]

15. Sharp measure contraction property for generalized H-type Carnot groups (with D. Barilari) - Communications in Contemporary Mathematics (in press) - [PDF]

*Memoirs of the AMS*(in press) - [PDF]2. How many geodesics join two points on a contact sub-Riemannian manifold? (with A. Lerario) -

*Journal of symplectic geometry*- [PDF]3. Comparison theorems for conjugate points in sub-Riemannian geometry (with D. Barilari) -

*ESAIM: Control, Optimisation and Calculus of Variations*- [PDF]4. On conjugate times of LQ optimal control problems (with A. Agrachev and P. Silveira) -

*Journal of Dynamical and Control Systems*- [PDF]5. A formula for Popp's volume in sub-Riemannian geometry (with D. Barilari) -

*Analysis and Geometry in Metric Spaces*- [PDF]6. Sub-Riemannian curvature in contact geometry (with A. Agrachev and D. Barilari) -

*Journal of Geometric Analysis*- [PDF]7. Measure contraction properties of Carnot groups -

*Calculus of Variations and Partial Differential Equations*- [PDF]8. On the cut locus of free, step two Carnot groups (with U. Serres) - Proceedings of the AMS - [PDF]

9. On Jacobi fields and a canonical connection in sub-Riemannian geometry (with D. Barilari) -

*Archivum Mathematicum*- [PDF]10. Intrinsic random walks and sub-Laplacians in sub-Riemannian geometry (with U. Boscain and R. Neel) -

*Advances in Mathematics*- [PDF]11. Intrinsic random walks in Riemannian and sub-Riemannian geometry via volume sampling (with A. Agrachev, U. Boscain and R. Neel) -

*ESAIM: Control, Optimisation and Calculus of Variations -*[PDF]12. Sub-Riemannian Ricci curvatures and universal diameter bounds for 3-Sasakian manifolds (with P. Silveira) -

*Journal of the Institute of Mathematics of Jussieu*- [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) -

*Journal of Differential Geometry*(in press) - [PDF]14. Quantum confinement on non-complete Riemannian manifolds (with D. Prandi and M. Seri) - Journal of Spectral Theory (in press) - [PDF]

15. Sharp measure contraction property for generalized H-type Carnot groups (with D. Barilari) - Communications in Contemporary Mathematics (in press) - [PDF]

## Submitted

16. Sub-Riemannian interpolation inequalities (with D. Barilari) - [Preprint]

17. On the essential self-adjointness of sub-Laplacians (with D. Prandi and V. Franceschi) - [Preprint]

18. A counterexample to gluing theorems for MCP metric measure spaces - [Preprint]

17. On the essential self-adjointness of sub-Laplacians (with D. Prandi and V. Franceschi) - [Preprint]

18. A counterexample to gluing theorems for MCP metric measure spaces - [Preprint]

## Published (physics)

18. Dielectric black holes induced by a refractive index perturbation and the Hawking effect (with F. Belgiorno, S.L. Cacciatori, G. Ortenzi, V. Gorini, D. Faccio) - Phys. Rev. D 83, 024015 (2011) - [PDF]

19. Hawking radiation from ultrashort laser pulse filaments (with F. Belgiorno, S.L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, E. Rubino, V.G. Sala, D. Faccio) - Phys. Rev. Lett. 105, 203901 (2010) - [PDF]

20. Spacetime geometries and light trapping in travelling refractive index perturbations (with F. Belgiorno, S. L. Cacciatori, V. Gorini, G. Ortenzi, L. Rizzi, V. G. Sala, D. Faccio) - New J. Phys. 12 095021 - [PDF]

21. Dark matter effects in vacuum spacetime (with S. Cacciatori, V. Gorini, A. Kamenshchik, O.F. Piattella) - Phys. Rev. D 82, 027301 (2010) - [PDF]

22. The Step-Harmonic Potential (with O.F. Piattella, S.L. Cacciatori, V. Gorini) - Am. J. Phys. Volume 78, Issue 8, pp. 842 (2010) - [PDF]

23. Scattering and delay time for 1D asymmetric potentials: the step-linear and the step-exponential cases (with O.F. Piattella, S.L. Cacciatori, V. Gorini) - Revista Brasileira de Ensino de Física (2016) - [PDF]

19. Hawking radiation from ultrashort laser pulse filaments (with F. Belgiorno, S.L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, E. Rubino, V.G. Sala, D. Faccio) - Phys. Rev. Lett. 105, 203901 (2010) - [PDF]

20. Spacetime geometries and light trapping in travelling refractive index perturbations (with F. Belgiorno, S. L. Cacciatori, V. Gorini, G. Ortenzi, L. Rizzi, V. G. Sala, D. Faccio) - New J. Phys. 12 095021 - [PDF]

21. Dark matter effects in vacuum spacetime (with S. Cacciatori, V. Gorini, A. Kamenshchik, O.F. Piattella) - Phys. Rev. D 82, 027301 (2010) - [PDF]

22. The Step-Harmonic Potential (with O.F. Piattella, S.L. Cacciatori, V. Gorini) - Am. J. Phys. Volume 78, Issue 8, pp. 842 (2010) - [PDF]

23. Scattering and delay time for 1D asymmetric potentials: the step-linear and the step-exponential cases (with O.F. Piattella, S.L. Cacciatori, V. Gorini) - Revista Brasileira de Ensino de Física (2016) - [PDF]

## About my research activity

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. This is why my "production" is split in physics (published in 2010-2011) and mathematics (2012 onward).

## PhD Thesis

The curvature of optimal control problems with applications to sub-Riemannian geometry - SISSA - Trieste, May 2014 - (Thesis - Slides)

## Some slides & Talks

- Metric Measure Spaces and Ricci Curvature - Bonn September 2017 - "Sub-Riemannian interpolation inequalities" (Slides)
- Bern Mathematical Colloquium - Bern University, December 2016 - "Some topics in sub-Riemannian geometry" (Slides)
- Groupe de Travail Contrôle - LJLL - UPMC, Paris, November 2015 - "Curvature: a variational approach" (Notes)
- Geometry & Control seminar - SISSA - Trieste, October 2015 - "A sub-Riemannian Santaló formula and applications" (Notes)
- Geometry & Control seminars - SISSA - Trieste, October 2015 - "Intrinsic random walks with volume sampling in Riemannian and sub-Riemannian geometry" (Slides)
- 2015 SIAM Conference on Control and Its Applications - Paris, July 2015 - "Intrinsic random walks and diffusion in sub-Riemannian geometry" (Abstract - Slides)
- IHP - Séminaire de géométrie sous-Riemannienne - Paris 21 May 2015 - "Intrinsic random walks and diffusion in sub-Riemannian geometry"
- RICAM - Geometric control and related fields - Linz, November 2014 - "The curvature, a variational approach"
- IHP - Thematic day Optimal transport and sub-Riemannian manifolds - Paris, October 2014 - "On measure contraction properties of sub-Riemannian manifolds"
- Geometric control theory and analysis on metric structures - Lake Baikal - (Slides)
- Institut Camille Jordan - Lyon, June 2014 - (Abstract)
- Steklov Mathematical Institute - Geometry and Control - Moscow, April 2014 (Video)
- SISSA - Mathematical Control in Trieste, Trieste, December 2013 (Abstract - Slides)
- IHP - Séminaire de géométrie sous-Riemannienne, Paris, October 2013 (Abstract - Slides)
- ICTP-SISSA-Moscow School on Geometry and Dynamics, Trieste, June 2013. (Outline)
- Nonlinear Control: geometric approach and applications, Florence, April 2013. (Abstract - Slides)