Dr Alessio Martini PhD

Dr Alessio Martini

School of Mathematics
Senior Lecturer in Mathematical Analysis

Contact details

School of Mathematics
Watson Building
University of Birmingham
B15 2TT

Alessio Martini is a Senior Lecturer and a member of the Mathematical Analysis Research Group in the School of Mathematics.


  • PhD in Mathematics, Scuola Normale Superiore (Pisa, Italy), 2010
  • Diploma di Licenza in Mathematics, Scuola Normale Superiore (Pisa, Italy), 2007
  • MSc in Mathematics, University of Pisa (Italy), 2006
  • BSc in Mathematics, University of Pisa (Italy), 2004


Alessio Martini studied Mathematics in Pisa (Italy), where he was simultaneously a student of the Università di Pisa and of the Scuola Normale Superiore (SNS). After obtaining a Master’s degree in 2006, he went on to study for a PhD in Mathematics at the SNS, followed by postdoctoral positions at the SNS, the University of New South Wales (Sydney, Australia), and the Christian-Albrechts-Universität zu Kiel (Germany). He was awarded a Research Fellowship of the Alexander von Humboldt Foundation and a research grant from the Deutsche Forschungsgemeinschaft (DFG). Alessio joined the School of Mathematics here at Birmingham in 2014.


Teaching Programmes

  • Single Honours Mathematics (G100, G103, G141)
  • Mathematics Majors: Mathematics with Business Management (G1N2); Mathematics with Engineering (J920); Mathematics with Philosophy (G1V5)
  • Joint Honours Mathematics: Mathematics & Computer Science (GG14); Pure Mathematics & Computer Science (GGC4); Mathematics & Sport Science (GC17); Mathematics & Music (GW13); Mathematics & Philosophy (GV15)
  • Theoretical Physics and Applied Mathematics (FG31)
  • Mathematics Minors: French Studies and Mathematics (GR11); German Studies and Mathematics (GR12)
  • Natural Sciences (CFG0, FCG0)

Postgraduate supervision

Dr Martini is interested in supervising doctoral research students in harmonic analysis and related topics.


Alessio's main area of research is harmonic analysis on Lie groups and their homogeneous spaces. This area is characterised by a strong interplay between techniques of functional analysis and Euclidean harmonic analysis and results from algebra and representation theory.

Alessio has worked on uncertainty inequalities and on spectral theory for commuting systems of differential operators. Recently he has been interested in the problem of obtaining sharp spectral multiplier theorems for non-elliptic hypoelliptic operators, such as sublaplacians, which arise naturally in non-commutative contexts.


Recent publications


Horwich, A & Martini, A 2021, 'Almost everywhere convergence of Bochner-Riesz means on Heisenberg-type groups', Journal of the London Mathematical Society, vol. 103, no. 3, pp. 1066-1119. https://doi.org/10.1112/jlms.12401

Martini, A, Meda, S & Vallarino, M 2021, 'Maximal characterisation of local Hardy spaces on locally doubling manifolds', Mathematische Zeitschrift. https://doi.org/10.1007/s00209-021-02856-x

Martini, A & Vallarino, M 2021, 'Riesz transforms on solvable extensions of stratified groups', Studia Mathematica, vol. 259, no. 2, pp. 175-200. https://doi.org/10.4064/sm190927-4-1

Martini, A, Müller, D & Nicolussi Golo, S 2021, 'Spectral multipliers and wave equation for sub-Laplacians: lower regularity bounds of Euclidean type', Journal of the European Mathematical Society. <https://arxiv.org/abs/1812.02671>

Casarino, V, Ciatti, P & Martini, A 2021, 'Uniform pointwise estimates for ultraspherical polynomials', Comptes Rendus Mathematique.

Casarino, V, Ciatti, P & Martini, A 2021, 'Weighted spectral cluster bounds and a sharp multiplier theorem for ultraspherical Grushin operators', International Mathematics Research Notices. https://doi.org/10.1093/imrn/rnab007

Martini, A, Meda, S & Vallarino, M 2020, 'A family of Hardy type spaces on nondoubling manifolds', Annali di Matematica Pura ed Applicata, vol. 199, no. 5, pp. 2061-2085. https://doi.org/10.1007/s10231-020-00956-9

Dall'Ara, GM & Martini, A 2020, 'A robust approach to sharp multiplier theorems for Grushin operators', Transactions of the American Mathematical Society, vol. 373, no. 11, pp. 7533-7574. https://doi.org/10.1090/tran/7844

Ahrens, J, Cowling, M, Martini, A & Müller, D 2020, 'Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres', Mathematische Zeitschrift, vol. 294, no. 3-4, pp. 1659-1686. https://doi.org/10.1007/s00209-019-02313-w

Martini, A, Ottazzi, A & Vallarino, M 2019, 'A multiplier theorem for sub-Laplacians with drift on Lie groups', Revista Matematica Iberoamericana , vol. 35, no. 5, pp. 1501-1534. https://doi.org/10.4171/rmi/1090

Martini, A, Ricci, F & Tolomeo, L 2019, 'Convolution kernels versus spectral multipliers for sub-Laplacians on groups of polynomial growth', Journal of Functional Analysis, vol. 277, no. 6, pp. 1603-1638. https://doi.org/10.1016/j.jfa.2019.05.024

Casarino, V, Ciatti, P & Martini, A 2019, 'From refined estimates for spherical harmonics to a sharp multiplier theorem on the Grushin sphere', Advances in Mathematics, vol. 350, pp. 816-859. https://doi.org/10.1016/j.aim.2019.05.003

Cowling, M, Martini, A, Müller, D & Parcet, J 2019, 'The Hausdorff-Young inequality on Lie groups', Mathematische Annalen, vol. 375, no. 1-2, pp. 93-131. https://doi.org/10.1007/s00208-018-01799-9

Martini, A, Ottazzi, A & Vallarino, M 2018, 'Spectral multipliers for sub-Laplacians on solvable extensions of stratified groups', Journal d'Analyse Mathématique, vol. 136, no. 1, pp. 357-397. https://doi.org/10.1007/s11854-018-0063-6


Ciatti, P & Martini, A (eds) 2021, Geometric Aspects of Harmonic Analysis. Springer INdAM Series, vol. 45, Springer. https://doi.org/10.1007/978-3-030-72058-2

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