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.
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
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
Academic History
| 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
https://orcid.org/0009-0000-8896-9999Link opens in a new window
- 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. American Mathematical Monthly (accepted). https://arxiv.org/abs/2405.13463. This is an expository essay on various notions of convexity and their consequences in normed vector spaces and functional analysis.
Notes and Slides
- Introductory notes on Complex Analysis (aimed at second year undergraduates with a bit of multivariable calculus)
- Topics in Harmonic Analysis (lecture notes written for a reading course in 2020-2021)
Talks and Conferences
- The royal road to geometry: 2000 years of history of the Parallel Postulate. (05/06/2024) Postgraduate Seminar (Warwick)
- Lp continuity of spectral projections for for the 2d Dirichlet Laplacian under perturbations of the domain. (27/02/2024) PDE and Applications Seminar (Warwick)
- How (not) to sum a Fourier series in 2 dimensions. (27/09/2023) Guest talk at the Acoustics Research Institute of the Austrian Academy of Sciences (Vienna).
- Poster presentation at Strobl22: Harmonic Analysis and ApplicationsLink opens in a new window (Strobl, Austria, June 2022)
- A tourist's guide to the (first) incompleteness theorem (13/03/2023) Postgraduate Seminar (Warwick)
- The Lp convergence of Fourier series for Triangular Domains (13/06/2021) Postgraduate Seminar (Warwick)
- Guest speaker at "Universidade de Verán: MATEMÁTICAS: MOITO MÁIS QUE NÚMEROS!" , Universidade de Santiago de Compostela, 26-28 July, 2021.
Title: All functions are continuous! A provocative introduction to constructive analysis (Slides, no animations) - What is the difference between a circle and a square?Link opens in a new window (03/06/2021) SPAAM Seminar Series (Warwick).
This talk is an introduction to transference techniques which bridge the convergence of Fourier series and Fourier integrals.