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Ryan L. Acosta Babb

ProfileI am a 3rd Year PhD student under the supervision of Prof James RobisonLink opens in a new window, working on Lp convergence of eigenfunction expansions for second-order linear differential operators in the plane.

Previously, I completed a 4 year BSc in Mathematics and Philosophy with Specialism in Foundations and Logic at the University of Warwick, and then the MASt in Mathematical SciencesLink opens in a new window programme, undertaking a project on Scaling Limits for Random Gaussian Fields supervised by Dr Stefan AdamsLink opens in a new window.

I may be reached at r.[last name A]-[last name B] at

I am also one of the organisers of the Warwick Junior Analysis and Probability SeminarLink opens in a new window.
Research Interests

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! I am researching the Lp convergence of series of eigenfunctions on the disc, and equilateral, hemiequilateral and 45-90-45 triangles.
Praeterea, cum artis mathematicae operam non do, placet latine discere, legere, scribere ac loqui. (Plura de hoc sunt additura!)

Academic History

2020-2024 (Current) CDT in Mathematical Sciences University of Warwick
2019-2020 MASt in Matematical Sciences (Distinction) University of Warwick
2015-2019 BSc (Hons) in Philosophy and Mathematics with Specialism in Foundations and Logic University of Warwick


2022-2023 TA for MA3H3 Set TheoryLink opens in a new window
2021-2022 TA for MA3F1 Functional Analysis ILink opens in a new window and MA250 Introduction to PDELink opens in a new window
2020-2021 TA for MA359 Measure TheoryLink opens in a new window
2019-2020 TA for MA260 Norms, Metrics and TopologiesLink opens in a new window

MA260 Support Classes

Here is some material I discussed during the Support Class for Norms, Metrics and Topologies:

DISCLAIMER: This material is my own and I take full responsibility for its content and any mistakes it may contain. It has not been revised by the lecturers or any other member of the department.


Notes and Slides

Talks and Conferences