Ryan L. Acosta Babb

University of Warwick

On the Shafberg
St. Wolfgang, Austria

Welcome!

I am a Teaching Fellow at the Warwick Mathematics Institute, where I completed my PhD under the supervision of Prof. James Robinson, working on Lp convergence of eigenfunction expansions for second-order linear differential operators in the plane.

In December 2025, I will move to Stockholm University with a Sverker Lerhed Fellowship.

Previously, I obtained a BSc in Mathematics and Philosophy with Specialism in Foundations and Logic at the University of Warwick, and then an MASt in Mathematical Sciences, undertaking a project on scaling limits for the Gaussian Free Field, supervised by Dr Stefan Adams.

I may be reached at: ryan.l.acosta-babb at warwick.ac.uk

Research interests

I am mainly interested in Harmonic Analysis and PDE, especially questions of convergence of Fourier series and their relatives.

In one dimension, there is only one way to truncate a partial sum: count up to a certain N. For eigenfunctions labelled by pairs of indices, as is the case of the Fourier series on Z2, we may truncate in several ways. For example, do we count pairs of indices (n, m) with |n|,|m| ≤ N, or instead count them with n2 + m2 ≤ N? It is a curious fact that Lp convergence can be obtained in the former case (for all p) but 'never' the latter: it fails for all p ≠ 2!

After proving new convergence results for triangular domains, I am studying how this convergence might be established in more general regions as they are deformed by homeomorphisms. For a list of publications, see my Research page.

American Mathematical Monthly

I am an Associate Editor of the American Mathematical Monthly.

Warwick Junior Analysis Seminar

I used to organise the Warwick Junior Analysis and Probability Seminar.

Page updated

Google Sites

Report abuse