Dr Alessio Martini PhD

Dr Alessio Martini

School of Mathematics
Senior Lecturer in Mathematical Analysis

Contact details

Address
School of Mathematics
Watson Building
University of Birmingham
Edgbaston
Birmingham
B15 2TT
UK

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

Qualifications

  • 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

Biography

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

Teaching Programmes

  • Single Honours Mathematics (G100, G103, G141)
  • Mathematics Majors: Mathematics with Business Management (G1N2); Mathematics with Engineering (J920); Mathematics with Philosphy (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.

Research

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.

Publications

Recent publications

Article

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, 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

Martini, A, Ottazzi, A & Vallarino, M 2019, 'A multiplier theorem for sub-Laplacians with drift on Lie groups', Revista Matematica Iberoamericana . https://doi.org/10.4171/rmi/1090

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

Ahrens, J, Cowling, M, Martini, A & Müller, D 2019, 'Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres', Mathematische Zeitschrift, pp. 1-28. https://doi.org/10.1007/s00209-019-02313-w

Dall'Ara, GM & Martini, A 2019, 'A robust approach to sharp multiplier theorems for Grushin operators', Transactions of the American Mathematical Society.

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

Casarino, V, Cowling, M, Martini, A & Sikora, A 2017, 'Spectral multipliers for the Kohn Laplacian on forms on the sphere in Cn', Journal of Geometric Analysis, vol. 27, no. 4, pp. 3302-3338. https://doi.org/10.1007/s12220-017-9806-3

Martini, A 2017, 'Joint functional calculi and a sharp multiplier theorem for the Kohn Laplacian on spheres', Mathematische Zeitschrift, vol. 286, no. 3-4, pp. 1539-1574. https://doi.org/10.1007/s00209-016-1813-8

Martini, A & Müller, D 2016, 'Spectral multipliers on 2-step groups: topological versus homogeneous dimension', Geometric and Functional Analysis, vol. 26, no. 2, pp. 680-702. https://doi.org/10.1007/s00039-016-0365-8

Martini, A 2015, 'Spectral multipliers on Heisenberg-Reiter and related groups', Annali di Matematica Pura ed Applicata, vol. 194, no. 4, pp. 1135-1155. https://doi.org/10.1007/s10231-014-0414-6

Martini, A & Müller, D 2014, 'A sharp multiplier theorem for Grushin operators in arbitrary dimensions', Revista Matematica Iberoamericana , vol. 30, no. 4, pp. 1265-1280. https://doi.org/10.4171/RMI/814

Martini, A & Müller, D 2014, 'Spectral multiplier theorems of Euclidean type on new classes of two-step stratified groups', London Mathematical Society. Proceedings , vol. 109, no. 5, pp. 1229-1263. https://doi.org/10.1112/plms/pdu033

Martini, A & Müller, D 2013, 'Lp spectral multipliers on the free group N3,2', Studia Mathematica, vol. 217, no. 1, pp. 41-55. https://doi.org/10.4064/sm217-1-3

Chapter

Cowling, M & Martini, A 2013, Sub-Finsler geometry and finite propagation speed. in MA Picardello (ed.), Trends in Harmonic Analysis. Springer INdAM Series, vol. 3, Springer, pp. 147-205. https://doi.org/10.1007/978-88-470-2853-1_8

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