I am currently working on topics related to the Fourier restriction and Kakeya conjectures.
The restriction/Kakeya link has been extremely fruitful and has contributed significantly to recent advances in areas like harmonic analysis and geometric measure theory. Certain multilinear versions of the conjectures have emerged and work of Bennett, Carbery and Tao (Acta Math. 2006) in particular has had a profound influence. Multilinear Kakeya estimates may be interpreted as a perturbation of the Brascamp-Lieb (BL) inequality. The BL inequality is a wide-reaching generalization of Hölder's inequality, Young's convolution inequality and the Loomis-Whitney inequality, and in addition to contributing significantly to recent progress on the restriction and Kakeya conjectures, the BL inequality has rich connections with many other fields, such as convex geometry, information theory, optimization theory, and theoretical computer science.
In the study of dispersive PDE such as the Schrödinger equation, Strichartz estimates are a family of estimates which provide control on the size and decay of the solution. Estimates of this type have had an enormous impact on the theory of dispersive PDE and the development of Strichartz-type estimates has also profited greatly from direct connections with the restriction and Kakeya conjectures. My research has predominantly focused on topics like those mentioned above. Most recently, various problems related to the BL inequality have particularly caught my attention.

1. N. Bez, A. Gauvan, H. Tsuji, A note on ubiquity of geometric Brascamp-Lieb data, Bull. Lond. Math. Soc. 57 (2025), 302-314.
2. N. Bez, S. Nakamura, H. Tsuji, Stability of hypercontractivity, the logarithmic Sobolev inequality, and Talagrand's cost inequality, J. Funct. Anal. 285 (2023), 110121.
3. N. Bez, S. Lee, S. Nakamura, Strichartz estimates for orthonormal families of initial data and weighted oscillatory integral estimates, Forum of Math. Sigma 9 (2021), e1 (52pp).
4. J. Bennett, N. Bez, S. Buschenhenke, M. G. Cowling, T. C. Flock, On the nonlinear Brascamp-Lieb inequality, Duke Math. J. 169 (2020), 3291-3338.
5. J. Bennett, N. Bez, Generating monotone quantities for the heat equation, J. Reine Angew. Math. 756 (2019), 37-63.
6. J. Bennett, N. Bez, T. C. Flock, S. Lee, Stability of the Brascamp-Lieb constant and applications, Amer. J. Math. 140 (2018), 543-569.
7. N. Bez, H. Saito, M. Sugimoto, Applications of the Funk-Hecke theorem to smoothing and trace estimates, Adv. Math. 285 (2015), 1767-1795.
8. N. Bez, K. M. Rogers, A sharp Strichartz estimate for the wave equation with data in the energy space, J. Eur. Math. Soc. 15 (2013), 805-823.

Mathematical Society of Japan, London Mathematical Society

2022- Journal of the Mathematical Society of Japan (editor)

2022 Mathematical Society of Japan Spring Prize

2020 MEXT Commendation for Science and Technology Young Scientists' Prize

2018 Journal of the Mathematical Society of Japan Outstanding Paper Prize

2014 Mathematical Society of Japan Takebe Katahiro Prize