Ryan L. Acosta Babb
I am a 3rd 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.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 warwick.ac.uk.
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.
Alia
Praeterea, cum artis mathematicae operam non do, placet latine discere, legere, scribere ac loqui. (Plura de hoc sunt additura!)
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 Mathematical Sciences (Distinction) | University of Warwick |
| 2015-2019 | BSc (Hons) in Philosophy and Mathematics with Specialism in Foundations and Logic | University of Warwick |
Teaching
| 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 (Accepted). Preprint of an earlier version: arXiv:2202.06119Link opens in a new window.
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
- 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)
- 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 at the University of Warwick.
This talk is an introduction to transference techniques which bridge the convergence of Fourier series and Fourier integrals.