# Jonathan Hickman

I am lecturer in the analysis group at the University of Edinburgh. Previously, I held postdoctoral positions in the University of Chicago, MSRI and the University of St Andrews. A CV can be found here.

### Research

My interests lie in Euclidean harmonic analysis, in particular questions pertaining to operators whose definition depends on some submanifold of $$\mathbb{R}^n$$ such as Fourier restriction/extension operators and generalised Radon transforms. I am also interested in discrete analogues of these objects.

### Papers: research

• The circular maximal operator on Heisenberg radial functions, with David Beltran, Shaoming Guo and Andreas Seeger, submitted. Preprint.

• Improved bounds for the Kakeya maximal conjecture in higher dimensions, with Keith Rogers and Ruixiang Zhang, submitted. Preprint.

• Uniform $$L^p$$ resolvent estimates on the torus, submitted. Preprint.

• On a higher dimensional version of the Benjamin--Ono equation, with Felipe Linares, Oscar G. Riaño, Keith Rogers and Jim Wright, to appear SIAM J. Math. Anal. Preprint.

• Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds, with David Beltran and Christopher D. Sogge, to appear Anal. PDE. Preprint.

• Sharp estimates for oscillatory integral operators via polynomial partitioning, with Larry Guth and Marina Iliopoulou, Acta Math., vol. 223, no. 2, pp. 251-376 (2019). Preprint.

• Counting factorisations of monomials over rings of integers modulo $$N$$, with Jim Wright, J. Théor. Nr. Bordx., vol. 31, no. 1, pp. 255-282, (2019). Preprint.

• Improved Fourier restriction estimates in higher dimensions, with Keith Rogers, Camb. J. Math., vol. 7, no. 3, pp. 219-282, (2019). Preprint.

• An abstract $$L^2$$ Fourier restriction theorem, with Jim Wright, Math. Res. Lett., vol. 26, no. 1, 75-100, (2019). Preprint.

• Some remarks on the Lipschitz regularity of Radon transforms, with Jonas Azzam and Sean Li, Proc. Amer. Math. Soc., vol. 146, no. 10, pp. 4331-4337, (2018). Preprint.

• The Fourier restriction and Kakeya problems over rings of integers modulo $$N$$, with Jim Wright, Discrete Analysis 2018:11, 54 pp, (2018). Preprint.

• Maximal operators and Hilbert transforms along variable non-flat homogeneous curves, with Shaoming Guo, Victor Lie and Joris Roos, Proc. Lond. Math. Soc. (3), vol. 115, pp. 177-219, (2017). Preprint.

• Uniform $$L^p_x - L^q_{x,r}$$ improving for dilated averages over polynomial curves, J. Funct. Anal., vol. 270, issue 2, pp. 560-608, (2016). Preprint.

• An affine Fourier restriction theorem for conical surfaces, Mathematika, vol. 60, issue 02, pp. 374-390, (2014). Preprint.

### Analysis seminar

I am currently the analysis seminar organiser. The seminar schedule can be found here.

### School colloquium

I am currently the school colloquium organiser. The colloquium schedule can be found here.

### Teaching

During 2019/2020 I am teaching the following courses:

### Contact

E-mail: jonathan.hickman [at] ed [dot] ac [dot] uk