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!
|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.
- Week 3 [22/01/20]: Uniform Continuity Handout
Notes and slides
- Introductory notes on Complex Analysis (aimed at second year undergraduates with a bit of multivariable calculus)
- All functions are continuous! A provocative introduction to constructive analysis (Slides, no animations)