Jonathan Hickman

Me

I am currently an L. E. Dickson Instructor in the University of Chicago. I completed my PhD in the University of Edinburgh under the supervision of Prof. Jim Wright. A brief 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

Maximal operators and Hilbert transforms along variable non-flat homogeneous curves, with Shaoming Guo, Victor Lie and Joris Roos, submitted. Preprint.

Some remarks on the Lipschitz regularity of Radon transforms, with Jonas Azzam and Sean Li, submitted. Preprint.

Uniform \(L^p_x - L^q_{x,r}\) Improving for Dilated Averages over Polynomial Curves, J. Funct. Anal., volume 270, issue 2, pp. 560608. Preprint.

An affine Fourier restriction theorem for conical surfaces, Mathematika, volume 60, issue 02, pp. 374-390. Preprint.



Teaching

I am currently lecturing Math 153 Calculus and Math 273 Basic Theory of Ordinary Differential Equations.

During 2015-2016 I lectured the Math 160 Honours Calculus series and Math 256 Algebra.

Expository notes

Together with Marco Vitturi and Odysseas Bakas I presented a series of lectures describing Bourgain and Demeter's recent work on Wolff-type decoupling inequalities: Lecture 1, Lecture 2, Lecture 3, Lecture 4, Lecture 5.

I also have some (somewhat rougher) notes on generalised Radon transforms, which were written to accompany a course I gave in the Analysis Working Group in Edinburgh: Lecture 1, Lecture 2, Lecture 3, Lecture 4, Picture 1, Picture 2.

I once wrote an essay on Furstenberg's proof of Szemeredi's theorem.

Here are slides from expository talks on Szemeredi's theorem, Roth's theorem and Kakeya sets.

I'd be grateful to hear about any mistakes / typos!

Contact

E-mail: jehickman [at] uchicago [dot] edu

Address:
Eckhart Hall Room 414,
Department of Mathematics,
University of Chicago,
5734 S. University Avenue,
Chicago,
Illinois,
60637.