Ryan L. Acosta Babb

University of Warwick

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.