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.

My main areas of research are:

• Metric Geometry,
• Geometric Measure Theory,
• Lie Group Theory,
• sub-Riemannian Geometry,
• Analysis on Metric Spaces,
• (a little bit in) Harmonic Analysis.

Primarily, I study Lie groups equipped with non-Riemannian distances such as Carnot-Carathéodory distances. Carnot-Carathéodory Geometry, also called sub-Riemannian Geometry, deals with geometric spaces of fractal nature arising from several contexts, such as Hyperbolic Geometry, Geometric Group Theory, Theory of Hypoelliptic Operators and Control Theory.

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.

Since September 2023, I am taking a break from the academic career.

If you want to know more about me, here is my CV. If you want to contact me, you can write me an email to sebastiano2.72@gmail.com. My ORCID ID is: 0000-0002-3773-6471.

Special Pages

• A tentative bibliographic list for BV functions on Carnot groups
• Interactions between Geometric measure theory, Singular integrals, and PDE
  Trimester Program (January 10 – April 22, 2022), Bonn
• Jyväskylä Geometric Analysis Seminar
• Lettura della sera
• GeA: seminario di Geometria e Analisi a Padova.
• Sub-Riemannian Geometry and Beyond, III: A gist on Lie groups in Pisa.
  (Postponed because of Covid-19 pandemy)
  Introductory courses: 19 May 2020 - 23 May 2020; http://crm.sns.it/event/462/
  The conference: 25 May 2020 - 29 May 2020; http://crm.sns.it/event/452/
• Miniworkshop Geometric Measure Theory in Padova.
• Latest in Geometric Analysis. Celebration of Pekka Koskela’s 59th birthday: in Będlewo (Poland), 24.11.2019 - 30.11.2019
• Didattica: “Analisi Matematica 1” per Ingegneria Meccanica, tenuto da Fabio Paronetto.

Publications

Preprints

• “Submanifolds with boundary and Stokes’ Theorem in Heisenberg groups”
  (with M. Di Marco, A. Julia, D. Vittone)
  [arxiv]
  
• “Moduli of Sub-Laplacians on the second Heisenberg group”
  (with B. Warhurst)
  [arXiv]
• “Curvature Exponent and Geodesic Dimension on Sard-regular Carnot groups”
  (with Y. Zhang)
  [arXiv]
• “Polarised Lie groups contactomorphic to stratified groups”
  (with A. Ottazzi)
  [arXiv]
• “Quasiregular mappings between subRiemannian manifolds”
  (with C.-Y. Guo, M. Williams)
  [arXiv]
• “From homogeneous metric spaces to Lie groups”
  (with M. G. Cowling, V. Kivioja, E. Le Donne, A. Ottazzi )
  [arXiv]

Published papers

1. “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]
2. “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]
3. “Jet spaces on 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.
4. “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]
5. “Lipschitz Carnot-Carathéodory structures and their limits”
   (with G. Antonelli and E. Le Donne)
   J. Dyn. Control. Syst. 29, 805–854 (2023) [Paper] [arXiv]
6. “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]
   
7. “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]
8. “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]
9. “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]
10. “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]
11. “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]
12. “Sub-Finsler horofunction boundaries of the Heisenberg group”
    (with N. Fisher)
    Analysis and Geometry in Metric Spaces, Volume 9, Issue 1 (2021)
    [Paper] [arXiv]
13. “Area-minimizing cones in the Heisenberg group \(\mathbb{H}^1\)”
    (with M. Ritoré)
    Annales Academiæ Scientiarum Fennicæ, Vol. 46 No. 2 (2021)
    [Paper] [arXiv]
14. “Metric Lie groups admitting dilations”
    (with E. Le Donne)
    Arkiv för Matematik Vol. 59, Issue 1, (Apr 2021) , pgs 125-163
    [Paper] [arXiv] [cvgmt]
15. “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]
16. “The Besicovitch covering property in the Heisenberg group revisited”
    (with S. Rigot)
    The Journal of Geometric Analysis, 29, 3345–3383 (2019)
    [Paper] [arXiv]
17. “Some remarks on contact variations in the first Heisenberg group”
    Ann. Acad. Sci. Fenn. Math., 43, 311–335 (2018)
    [Paper] [arXiv] [cvgmt]
18. “Regularity properties of spheres in homogeneous groups”
    (with E. Le Donne)
    Trans. Amer. Math. Soc., 370, 2057-2084 (2018).
    [Paper] [arXiv] [cvgmt]
19. “Topics in the geometry of non-Riemannian lie groups”
    PhD Thesis, University of Jyväskylä, 2017
    [Online]
20. “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]
21. “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

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