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Ryan Acosta Babb

ProfileI 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 Sciences programme, undertaking a project on Scaling Limits for Random Gaussian Fields supervised by Dr Stefan Adams.

Currently, I am a 2nd Year PhD student under the supervision of Prof James Robison, working on Lp convergence of eigenfunction expansions for second-order linear differential operators in the plane.

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 |n|2+|m|2 ≤ 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!

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


2020-2021 TA for MA359 Measure Theory
2019-2020 TA for MA260 Norms, Metrics and Topologies

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