In the summer of my second year at Oxford I did a research project supervised by Professor Terry Lyons.

My Motivation.

  I wanted to get a glimpse into what mathematical research was like; as an undergrad, this is surprisingly hard to understand just from the course! One of my mentors at the time, Prof. Rama Cont, suggested that a summer research project might help achieve this, so he set me up an interview. The interview was a success, and funding was found just in time. I was excited: by the end of the summer I'd have a far better awareness of what mathematical research entails!

The brief.

'You have a signal that is (to start with) zero and then 1000 electromagnetic waves sine waves and then zero. In fact, the period of the signal is 1ghz, or 30cm wavelength. It hits and reflects off two moving objects: one at low speed (a drone) and a second rotating device (a propellor spinning on the drone). Challenge 1: make a very simple model for the reflected signal observed at the source. Then we want to align it with the delayed original signal to create a 2D path. This happens 8000 times a second. We want to look at these paths and see if we can (use signatures to) see the speed of the blades etc.'

The project.

  I was brilliantly equipped for this project: I had no understanding of how to start researching, and no Python knowledge (something it turned out that I needed...). Oh, and I'd only chosen any pure maths courses so far, but the project was very applied. This meant that I didn't know what a model was, let alone how to create one (even if it only needed to be 'very simple'). Sounds like a recipe for success to me! 😂

  Whilst I was simply emailed the quoted brief above, others doing different projects had been given research papers to start reading. I took inspiration, and started reading papers (after Googling what a model was...). Somehow, after half a Codecademy course, lots of reading, and some much-needed help from Terry's PhD student Cris, I made some progress! It wasn't a complete project, but it was something.

  Peter Foster tidied up and finished the project, and it's now an example on the Datasig website: Identifying Drones. In particular, here's the write-up on GitHub: Path Signatures for Drone Identification using esig.

My advice.

  If you're a current student about to embark on your first research project, my advice is to not worry! Take it slowly, and don't hesitate to ask for help when you need it. It might feel like you're making no progress, but you will eventually. Good luck! :)