Welcome to my academic story.
I became a Doctor of Mathematics back in 2025, after 4+ years of a PhD and following academic research on my specialist subject as early as 2019. I studied at Imperial College London under supervisor Dr Eva-Maria Graefe as an applied mathematician, bringing together expertise on maths, physics, quantum, dynamics, coding, numeric, analysis and tackling theorical and real world problems. Answering big questions for why the universe acts the way it does, and problems that are equal parts fun and foundational. I was also a research assistant briefly, studying optical wave guides (basically fibre optics), and proudly co-organised an international conference for the university.

I love sharing my knowledge gained from my PhD, but where do I begin?
Well, consider my research to have formed two big icebergs… these two icebergs:
Left: One iceberg is all about how things move, where we care about getting an idea for that things position and momentum. This gets tricky when that thing is tiny and can lose energy.
Right: The other iceberg is about billiards! You know, that thing you find in a pub. Some crazy stuff can happen when you decide to make billiard tables not-rectangular.

Interested in the technicalities or just want to see very pretty simulations? Here are the published papers:

Husimi Dynamics Generated by non-Hermitian Hamiltonians
Physical Review Letter: journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.157202
Free open source Arxiv version: arxiv.org/abs/2212.03719

Intensity landscapes in elliptical and oval billiards with a circular absorbing region
Physical Review E: journals.aps.org/pre/abstract/10.1103/9bv6-4npn
Free open source Arxiv version: arxiv.org/abs/2411.08694

I also included a lot of research into my PhD thesis before I finished university to start my career as a trainer and facilitator.
Free open source Thesis: spiral.imperial.ac.uk/entities/publication/9925ac56-de94-4575-925f-a0167b8a2c67

Invitation to talk science!
Plus there is a lot more to the icebergs, spin-off tiny icebergs and weird little disconnected icebergs too!
You get up to many things during a 4+ year PhD.
If you want to go further down any iceberg with me, then pop me a message at Hello@DrKatherineHolmes.com.

I am also educated in various specialist topics from maths and physics, quantum computing and optics to computer science and numerical analysis; and continue to learn from experts about life sciences, environmental and social policy, AI/ML, technology and much more. Oh, and of course, what my work now is based on – communication theory and practice (but more detail on that across my other webpages).