Professor Jonathan Bennett BA PhD

Professor Jonathan Bennett

School of Mathematics
Professor of Mathematical Analysis

Contact details

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

Jonathan is a Mathematical Analyst, specialising in Harmonic Analysis and its interactions with a variety of other branches of Mathematics. He is a member of the Analysis Group in the School of Mathematics.

Jonathan has received research grants from the EPSRC and ERC. In 2011 he received a Whitehead Prize from the London Mathematical Society for his contributions to Geometric and Harmonic Analysis.

Qualifications

  • PhD in Harmonic Analysis, University of Edinburgh, 1999
  • BA in Mathematics, University of Oxford, 1995

Biography

Jonathan Bennett qualified with a first class BA (Hons) in Mathematics from Hertford College, Oxford in 1995. He went on to study for a PhD in Harmonic Analysis at the University of Edinburgh, followed by postdoctoral positions at the University of Edinburgh, the Universidad Autonoma de Madrid and Trinity College Dublin. Jonathan joined the School of Mathematics here at Birmingham in 2005.

Teaching

Semester 1

LC Sequences and Series

Semester 2

LH/LM Functional and Fourier Analysis

Postgraduate supervision

Jonathan is interested in supervising doctoral research students in all aspects of Euclidean Harmonic Analysis.

Research

Research Themes

  • Harmonic Analysis

Research Activity

Jonathan's main interests lie in multivariable Euclidean harmonic analysis and its interactions with geometric analysis, partial differential equations and combinatorial geometry. Recently he has been investigating the scope of heat-flow techniques, induction-on-scales arguments, and tomographic methods in the restriction theory of the Fourier transform. Of particular interest to Jonathan are the many ways in which oscillatory phenomena, such as bounds on oscillatory integral operators, are governed by underlying geometric notions such as curvature or transversality.

Other activities

Editor for the Quarterly Journal of Mathematics (2018-present)

Analysis Editor for Mathematika (2016-present)

Editorial Adviser for the Proceedings, Journal, Bulletin and Transactions of the London Mathematical Society (2008-2016).

Analysis Subject Editor for the Proceedings of the Edinburgh Mathematical Society (2007-2012)

Organiser of the LMS/ERC-funded “UK Harmonic Analysis and PDE Research Network” (2005-2014)

Publications

Recent publications

Article

Bennett, J & Jeong, E 2021, 'Fourier duality in the Brascamp-Lieb inequality', Mathematical Proceedings of the Cambridge Philosophical Society, pp. 1-23. https://doi.org/10.1017/S0305004121000608

Bennett, J & Nakamura, S 2021, 'Tomography bounds for the Fourier extension operator and applications', Mathematische Annalen, vol. 380, no. 1-2, pp. 119–159. https://doi.org/10.1007/s00208-020-02131-0

Aoki, Y, Bennett, J, Bez, N, Machihara, S, Matsuura, K & Shiraki, S 2020, 'A supersolutions perspective on hypercontractivity', Annali di Matematica Pura ed Applicata, vol. 199.

Bennett, J, Bez, N, Buschenhenke, S, Cowling, MG & Flock, TC 2020, 'On the nonlinear Brascamp-Lieb inequality', Duke Mathematical Journal, vol. 169, no. 17, pp. 3291-3338. https://doi.org/10.1215/00127094-2020-0027

Bennett, J & Bez, N 2019, 'Generating monotone quantities for the heat equation', Journal fuer die Reine und Angewandte Mathematik: Crelle's journal , vol. 2019, no. 756, pp. 37–63. https://doi.org/10.1515/crelle-2017-0025

Bennett, J & Iliopoulou, M 2018, 'A multilinear Fourier extension identity on Rn', Mathematical Research Letters, vol. 25, no. 4, pp. 1089-1108. https://doi.org/10.4310/MRL.2018.v25.n4.a2

Bennett, J, Bez, N, Flock, TC, Gutiérrez, S & Iliopoulou, M 2018, 'A sharp k-plane Strichartz inequality for the Schrödinger equation', Transactions of the American Mathematical Society, vol. 370, no. 8, pp. 5617-5633 . https://doi.org/10.1090/tran/7309

Bennett, J, Bez, R, Gutierrez, S & Lee, S 2018, 'Estimates for the kinetic transport equation in hyperbolic Sobolev spaces', Journal de Mathematiques Pures et Appliquees , vol. 114, pp. 1-28. https://doi.org/10.1016/j.matpur.2018.03.007

Bennett, J, Bez, N, Flock, TC & Lee, S 2018, 'Stability of the Brascamp-Lieb constant and applications', American Journal of Mathematics, vol. 140, no. 2, pp. 543-569. https://doi.org/10.1353/ajm.2018.0013

Bennett, J, Bez, N, Cowling, MG & Flock, TC 2017, 'Behaviour of the Brascamp--Lieb constant', Bulletin of the London Mathematical Society, vol. 49, no. 3, pp. 512-518. https://doi.org/10.1112/blms.12049

Bennett, J, Bez, N, Jeavons, C & Pattakos, N 2017, 'On sharp bilinear Strichartz estimates of Ozawa-Tsutsumi type', Journal of the Mathematical Society of Japan, vol. 69, no. 2, pp. 459-476. https://doi.org/10.2969/jmsj/06920459

Beltran, D & Bennett, J 2017, 'Subdyadic square functions and applications to weighted harmonic analysis', Advances in Mathematics, vol. 307, pp. 72-99. https://doi.org/10.1016/j.aim.2016.11.018

Bennett, J, Bez, N & Iliopoulou, M 2015, 'Flow monotonicity and Strichartz inequalities', International Mathematics Research Notices, vol. 2015, no. 19, pp. 9415–9437. https://doi.org/10.1093/imrn/rnu230

Bennett, J 2014, 'Aspects of Multilinear Harmonic Analysis Related to Transversality', Contemporary Mathematics.

Bennett, J, Bez, N, Gutierrez, S & Lee, S 2014, 'On the Strichartz estimates for the kinetic transport equation', Communications in Partial Differential Equations, vol. 39, no. 10, pp. 1821-1826. https://doi.org/10.1080/03605302.2013.850880

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