I am a Senior Researcher at the Department of Mathematics of the University of Fribourg, in the Canton of Fribourg (in Switzerland), which is outside the European Union, but still on planet Earth.

If you want to contact me, you can write me an email to sebastiano2.72@gmail.com.

My main areas of research are:

  • Metric Geometry,
  • Geometric Measure Theory,
  • Lie Group Theory,
  • Sub-Riemannian Geometry,
  • Analysis on Metric Spaces,
  • Harmonic Analysis.

If you want to know more about me, here is my CV. My ORCID ID is: 0000-0002-3773-6471.

Special Pages

  • Course in Fribourg 2025: Partial Differential Equations
  • Sub-Riemannian Geometry and Beyond, IV in Schwarzsee (Fribourg, Switzerland), 23-27 of June 2025.
  • I have made a PDF calculator, with a bit of python and latex. It is a fully functional calculator modulus 100.
  • A notebook
  • There is a small but very energetic community of Buddhist monks and nuns on the hills of Parma. Their home is called Fudenji, the Temple of the Universal Teaching. The strict rule of their practice embrace everyone who knocks at their door, in the effort of following the Way, the way from me to you.
    In a world where equality is thought as the key of peace, while difference the key of war, they work every day between illusions and enlightment to make difference the key of our encouter. After forty years of exercise and construction, the moment has come to build what alone reunites earth and sky, past and future, ancestors and descendants: the Pagoda.

Publications

Preprints

  • “Asymptotics of Riemannian Lie groups with nilpotency step 2”
    (with E. L. Donne, L. Nalon, and S.-Y. Ryoo)
    [arxiv]
  • “Equivalence of sub-Laplacian on Polarized groups”
    (with A. Kijowski and B. Warhurst)
    [arxiv]
  • “Moduli of Sub-Laplacians on the second Heisenberg group”
    (with B. Warhurst)
    [arXiv]
  • “Quasiregular mappings between subRiemannian manifolds”
    (with C.-Y. Guo, M. Williams, and Y. Xuan)
    [arXiv]

Published papers

  1. “Submanifolds with boundary and Stokes’ Theorem in Heisenberg groups”
    (with M. Di Marco, A. Julia, D. Vittone)
    Trans. Amer. Math. Soc. (only published electronically, for now).
    [Paper] [arxiv]
  2. “From homogeneous metric spaces to Lie groups”
    (with M. G. Cowling, V. Kivioja, E. Le Donne, A. Ottazzi )
    C. R. Math. Acad. Sci. Paris 362 (2024), 943–1014.
    [Paper] [arXiv]
  3. “Curvature Exponent and Geodesic Dimension on Sard-regular Carnot groups”
    (with Y. Zhang)
    Anal. and Geom. in Metr. Spaces, vol. 12, no. 1, pp. 20240004 (2024)
    [Paper] [arXiv]
  4. “Left-invariant distributions diffeomorphic to flat distributions”
    (with A. Ottazzi)
    Geom Dedicata 218, 56 (2024)
    [Paper] [arXiv]
  5. “Classical flows of vector fields with exponential or sub-exponential summability”
    (with A. Ambrosio and F. Serra Cassano)
    J. Differ. Equations  372  458–504  (2023)
    [Paper] [arXiv]
  6. “Optimal $C^\infty$-approximation of functions with exponentially or sub-exponentially integrable derivative”
    (with A. Ambrosio and F. Serra Cassano)
    Calc. Var. Partial Differ. Equ.  62  21  (2023)
    [Paper] [arXiv]
  7. “Jet spaces over Carnot groups”
    (with B. Warhurst)
    Rev. Mat. Iberoam. 39 (2023), no. 6, pp. 2289–2330
    [Paper] [arXiv]
    I have written some python code to compute those jet spaces: see the page on github.
  8. “Nilpotent groups and biLipschitz embeddings into L1”
    (with S. Eriksson-Bique, C. Gartland, E. Le Donne, L. Naples)
    International Mathematics Research Notices, Volume 2023, Issue 12, June 2023, Pages 10759–10797
    [Paper] [arXiv]
  9. “Lipschitz Carnot-Carathéodory structures and their limits”
    (with G. Antonelli and E. Le Donne)
    J. Dyn. Control. Syst. 29, 805–854 (2023)
    [Paper] [arXiv]
  10. “Lipschitz functions on submanifolds in Heisenberg groups”
    (with A. Julia and D.Vittone)
    International Mathematics Research Notices, Volume 2023, Issue 9, May 2023, Pages 7399–7422
    [Paper] [arXiv]
  11. “Metric equivalences of Heintze groups and applications to classifications in low dimension”
    (with V. Kivioja and E. Le Donne)
    Illinois Journal of Mathematics Vol. 66, Issue 1, (Apr 2022) , pgs 91-121
    [Paper] [arXiv]
  12. “Area of intrinsic graphs and coarea formula in Carnot Groups”
    (with A. Julia and D. Vittone)
    Mathematische Zeitschrift, 301, 1369–1406 (2022).
    [Paper] [arXiv] [cvgmt]
  13. “Spectral multipliers and wave equation for sub-Laplacians: lower bounds of Euclidean type”
    (with A. Martini, D. Müller)
    Journal of the European Mathematical Society, 25 (2023), no. 3, pp. 785–843
    [Paper] [arXiv]
  14. “Nowhere differentiable intrinsic Lipschitz graphs”
    (with A. Julia and D. Vittone)
    Bulletin of the London Mathematical Society, Volume 53, Issue 6, December 2021, Pages 1766-1775
    [Paper] [arXiv]
  15. “Intrinsic rectifiability via flat cones in the Heisenberg group”
    (with A. Julia)
    Ann. Sc. Norm. Super. Pisa Cl. Sci., Vol. XXIII, Issue 2 (2022).
    [Paper] [arXiv] [cvgmt]
  16. “Sub-Finsler horofunction boundaries of the Heisenberg group”
    (with N. Fisher)
    Analysis and Geometry in Metric Spaces, Volume 9, Issue 1 (2021)
    [Paper] [arXiv]
  17. “Area-minimizing cones in the Heisenberg group \(\mathbb{H}^1\)”
    (with M. Ritoré)
    Annales Academiæ Scientiarum Fennicæ, Vol. 46 No. 2 (2021)
    [Paper] [arXiv]
  18. “Metric Lie groups admitting dilations”
    (with E. Le Donne)
    Arkiv för Matematik Vol. 59, Issue 1, (Apr 2021) , pgs 125-163
    [Paper] [arXiv] [cvgmt]
  19. “The Bernstein problem for Lipschitz intrinsic graphs in the Heisenberg group”
    (with F. Serra Cassano)
    Calculus of Variations and Partial Differential Equations, 58,  141  (2019)
    [Paper] [arXiv] [cvgmt]
  20. “The Besicovitch covering property in the Heisenberg group revisited”
    (with S. Rigot)
    The Journal of Geometric Analysis, 29, 3345–3383 (2019)
    [Paper] [arXiv]
  21. “Some remarks on contact variations in the first Heisenberg group”
    Ann. Acad. Sci. Fenn. Math., 43, 311–335 (2018)
    [Paper] [arXiv] [cvgmt]
  22. “Regularity properties of spheres in homogeneous groups”
    (with E. Le Donne)
    Trans. Amer. Math. Soc., 370, 2057-2084 (2018).
    [Paper] [arXiv] [cvgmt]
  23. “Topics in the geometry of non-Riemannian lie groups”
    PhD Thesis, University of Jyväskylä, 2017
    [Online]
  24. “Asymptotic behavior of the Riemannian Heisenberg group and its horoboundary”
    (with E. Le Donne, A. Sambusetti)
    Ann. Mat. Pura Appl., Volume 196, Issue 4, pp 1251–1272 (2017)
    [Paper] [arXiv] [cvgmt]
  25. “A historical account on characterizations of C^1-manifolds in Euclidean spaces by tangent cones”
    (with F. Bigolin)
    J. Math. Anal. Appl., 2014
    [Paper]

Collaborators and Friends

Gioacchino Antonelli
Francesco Bigolin
Michael G. Cowling
Damian Dąbrowski
Moon Duchin
Nate Fisher
Katrin Fässler
Chang-Yu Guo
Ville Kivioja
Enrico Le Donne
Alessio Martini
Detlef Müller
Tuomas Orponen
Alessandro Ottazzi
Séverine Rigot
Manuel Ritoré
Andrea Sambusetti
Raul Serapioni
Francesco Serra Cassano
Michele Villa
Ben Warhurst
Marshall Williams

Short Bio

I obtained a double PhD degree in 2017 from the University of Jyväskylä (Finland, EU) and from the University of Trento (Italy, EU), under the supervision of Enrico Le Donne and Francesco Serra Cassano. I later worked in Birmingham (UK) with Alessio Martini for one year, and in Padova (IT, EU) with Davide Vittone for one year and a half. From 2020 to 2023, I have been a postdoc at the Department of Mathematics and Statistics of the University of Jyväskylä in Finland (EU), under the supervision of Katrin Fässler and of Enrico Le Donne.

Then, I took a break in the academic year 2023–2024, when I lived in the Zen monastery Fudenji.

As of 2024, I am working in the academy, under the supervision of my boss, mentor and friend Enrico Le Donne.

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