Group report (October 2021)

As we enter the start of the 2021-22 academic term, it is time to bring our summer to a close, to celebrate the various comings and goings, and to look forwards to all sorts of new things.

First, we congratulate our MMath and BSc project students for completing their dissertations in such a difficult year. Ana Cassaniga Simmons did hers on “An introduction to complex ray theory and its applications”, Raban Braymuk did his on “Mathematical models in flooding”, and Henry Lockyer produced “On Escher's print gallery and its complex analytic structure”.

Henry's work won our departmental's inaugural dissertation prize for MMath students.

We will probably welcome at least another new MMath student to the group for 21-22. TBD…

Complex ray image from Ana's work

Droste effect from Henry's work

In a twist of fate, we also congratulate Henry for securing a last-minute surprise PhD position with the SAMBa CDT at Bath. Since this email marks his official departure from our group, I guess Henry won't be on these mailing lists for 21-22, but perhaps we can attract him back in a year's time…

Now having completed their Thesis Formulation Reports (almost), Cecilie Andersen and Timothy Peters should be fully fledged PhD students soon. Cecilie will be doing a project on exponential asymptotics and selection mechanisms, while Timothy will be doing a project on developing mathematical models of ice crystal icing in engines.

Yyanis presented a seminar at the Isaac Newton Institute programme. Josh presented at the BAMC and IMA conferences his work on water waves. Edwin and Piotr also presented some very nice posters at the BAMC and UK Fluids Conference.

We had some very nice gatherings in the summer and fall. We can look forwards to more.

This year will be an interesting one. Research continues at a quick pace, and many of you are nearing completion of interesting research findings. In no particular order, here are some things I'm excited about:

1. Cecilie has been discovering all manner of subtleties in jet separation problems, and will hopefully help solve a big puzzle in exponential asymptotics regarding how surface tensions selects an angle of separation;
2. Timothy has been working on extending recent ice crystal models to include behaviours of fluids on curved surfaces; we have high hopes that this will form the basis of a substantial new model.
3. Piotr is preparing a pair of significant papers on fundamental development of mathematical models for flood modelling;
4. Edwin has been probing into some deep questions about the snaking behaviours of discrete and continuum systems of pattern formation;
5. Josh is knee-deep in about four different sub-projects that are all near completion in some manner; these include mathematical models for optical fibre tunnelling and problems related to geophysical instabilities—these have somehow been developed as side projects to understand mathematics within his main strand of work.
6. Yyanis continues some excellent work on ray theory and the development of theory for wave-structure interactions; and finally
7. Sam brings a new host of tools and thinking to our group. At the moment, he pursues some problems in developing alternative techniques (Borel transformation, Pichard-Lefschetz theory) to more fiendishly difficult asymptotics problems (higher-dimensional in some sense).