Ryan L. Acosta Babb

I am a 4th Year PhD student under the supervision of Prof James RobinsonLink opens in a new window, working on Lp convergence of eigenfunction expansions for second-order linear differential operators in the plane. I am currently applying for postdocs.

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 the Gaussian Free Field, supervised by Dr Stefan AdamsLink opens in a new window.

I may be reached at r.[last name A]-[last name B] at warwick.ac.uk. | Personal SiteLink opens in a new window

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!
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.
Lingua Latina
Praeterea, cum arti mathematicae operam non do, placet latine discere, legere, scribere ac loqui.
Hic colloquium audire potestis de Cursu Æestivo Latinitatis Vivae Matritensi: https://youtu.be/4ncHOGn15KA

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

Teaching

 2023-2024 TA for MA3B8 Complex Analysis and PH201 History of Modern Philosophy (Part II: Kant) 2022-2023 TA for MA3H3 Set TheoryLink opens in a new window and MA260 Norms, Metrics and TopologiesLink 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.

Publications and preprints

• R. L. Acosta Babb (2023) The Lp convergence of Fourier series on triangular domains. Proceedings of the Edinburgh Mathematics Society. https://doi.org/10.1017/S0013091523000226
• R. L . Acosta Babb (2023) Remarks on the Lp convergence of Bessel–Fourier series on the disc. Comptes Rendus Mathématiques. https://doi.org/10.5802/crmath.464
• R. L. Acosta Babb and J. C. Robinson (submitted) Lp continuity of eigenprojections for 2-d Dirichlet Laplacians under domain perturbations. https://arxiv.org/abs/2401.10066Link opens in a new window
• R. L. Acosta Babb. Exploring convexity in normed spaces (submitted). This is an expository essay on various notions of convexity and their consequences in normed vector spaces and functional analysis.