# Professor Jonathan Bennett BA, PhD

School of Mathematics

Professor of Mathematical Analysis

## Contact details

- Telephone
- +44 (0) 121 414 6579
- Fax
- +44 (0) 121 414 3389
- j.bennett@bham.ac.uk

- 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, which conducts research in a wide variety of interconnected areas.

Jonathan has numerous publications in leading international mathematical journals and has received major research grants from the EPSRC. Jonathan currently holds an ERC Starting Grant entitled Transversal Multilinear Harmonic Analysis. In 2011 Jonathan received a Whitehead Prize from the London Mathematical Society for his contributions to Geometric and Harmonic Analysis.

## Qualifications

Professor in Pure Mathematics:

- 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

- 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

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

## Research

### Research Themes

Harmonic Analysis ### Research Activity

Jonathan’s interests lie in multivariable Euclidean harmonic analysis and its interactions with problems in geometric analysis and combinatorics. Recently he has been investigating the scope of heat-flow methods and induction-on-scales arguments in the analysis of geometric inequalities arising in the restriction theory for 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

### Selected publications:

- Bennett, J., Carbery, A., Wright, J. (2005), A nonlinear generalisation of the Loomis-Whitney inequality and applications, Math. Res. Lett.,12 (4), pp.10001-10015.
- Bennett, J., Carbery, A., Soria, F., Vargas, A. (2006), A Stein conjecture for the circle, Math. Annalen, 336, pp. 671-695.
- Bennett, J., Carbery, A., Tao, T. (2006), On the multilinear restriction and Kakeya conjectures, Acta Mathematica, 196, pp. 261-302.
- Barcelo, J.A., Bennett, J., Carbery, A., Ruiz, A., Vilela, M.C. (2007), Some special solutions of the Schroedinger equation, Indiana Univ. Math. J., 56, pp. 1581-1593.
- Bennett, J., Carbery, A., Christ, M., Tao, T. (2008), The Brascamp-Lieb Inequalities: Finiteness, Structure and Extremals, Geom. and Funct. Anal., 17, pp. 1343-1415.
- Bennett, J., Seeger, A. (2009), The Fourier extension operator on large spheres and related oscillatory integrals, Proc. Lond. Math. Soc., 98, pp. 45-82.
- Bennett, J., Bez, N., Carbery, A. (2009), Heat-flow monotonicity related to the Hausdorff-Young inequality, Bull. Lond. Math. Soc., 41, pp. 971-979.
- Bennett, J., Bez, N. (2009), Closure properties of solutions to heat inequalities, J. Geom. Anal., 19, pp. 584-600.
- Bennett, J., Bez, N., Carbery, A., Hundertmark, D. (2009), Heat-flow monotonicity of Strichartz norms, Analysis and PDE, 2 (2), pp.147-158.
- Bennett, J., Carbery, A., Christ, M., Tao, T. (2010), On multilinear inequalities of Brascamp-Lieb type, Math. Res. Lett. 17, pp. 647-666.
- Bennett, J. (2010), “Heat-flow monotonicity related to some inequalities in euclidean analysis”, In: Proceedings of the 8th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial, Spain. Contemporary Mathematics, 505, pp. 85-96.
- Bennett, J., Bez, N. (2010), Some nonlinear Brascamp-Lieb inequalities and applications to harmonic analysis, Journal of Functional Analysis, 259, pp. 2520-2556.
- Barcelo, J.A., Bennett, J., Carbery, A., Rogers, K. (2011), On the dimension of divergence sets of dispersive equations, Mathematische Annalen, 349, pp. 599-622.
- Bennett, J., Harrison, S. (2012), Weighted norm inequalities for oscillatory integrals with finite type phases on the line, Advances in Mathematics, 229, pp. 2159-2183.
- Bennett, J., Bez, N., Gutiérrez, S., (2013), Transversal multilinear Radon-like transforms: local and global estimates, Revista Matem’atica Iberoamericana, 29 (3), 765{788.
- Bennett, J., (2014), Aspects of multilinear harmonic analysis related to transversality, Contemporary Mathematics, 612, 1-28.
- Bennett, J., Bez, N., Gutiérrez, S., Lee, S., (2014), On the Strichartz estimates for the kinetic
- transport equation, Comm. PDE, 39, 1821-1826.
- Bennett, J., (2014), Optimal control of singular Fourier multipliers by maximal operators, Analysis & PDE, 7 (6), 1317-1338.
- Bennett, J., Bez, N., Iliopoulou, M., (2015), Flow monotonicity and Strichartz inequalities, International Mathematics Research Notices, 19, 9415{9437.
- Bennett, J., Bez, N., Flock, T., Lee, S., (2018), Stability of the Brascamp-Lieb constant and applications, Amer. J. Math., 140 (2), 543-569
- Bennett, J., Bez, N., (2019), Generating monotone quantities for the heat equation, Journal fur die reine und angewandte Mathematik: Crelle’s Journal, 756, 37-63
- Bennett, J., Bez, N., S. Gutierrez, Lee, S., (2018), Estimates for the kinetic transport equations in hyperbolic Sobolev spaces, J. Math. Pures Appl., 114, 1-28
- Bennett, J., Bez, N., Flock, T.C., Gutierrez, S., Iliopoulou, M., (2018), A sharp k-plane Strichartz inequality for the Schroedinger equation, Trans. Amer. Math. Soc., 370, 5617-5633
- Beltran, D., Bennett, J., (2017), Subdyadic square functions and applications to weighted harmonic analysis, Advances in Mathematics, 307 (2017), 72-99.
- Bennett, J., Iliopoulou, M., (2018), A multilinear Fourier extension identity on L2, Math. Res. Lett., 25 (4), 1089-1108
- Bennett, J., Bez, N., Cowling, M.G., Flock, T.C., (2017), Behaviour of the Brascamp-Lieb constant, Bull. Lond. Math. Soc., 49 (3), 512-518.
- Aoki, Y., Bennett, J., Bez, N., Machihara, S., Matsuura, K., Shiraki, S., (2020) A supersolutions perspective on hypercontractivity, Annali di Matematica, 199, 2105-2116.
- Bennett, J., Bez, N., Buschenhenke, S., Cowling, M.G., Flock, T.C., On the nonlinear Brascamp-Lieb inequality, to appear in Duke Math. J.
- Bennett, J., Nakamura, S., Tomography bounds for the Fourier extension operator and applications, to appear in Math. Annalen.