I’m George, I am a second year CMI student supervised by Matthew Colbrook and Anders Hansen. My Part III essay (~~which will appear here at some point~~ – I am now more likely to rewrite its content on here) was on computational impossibility results for the spectral problem for self-adjoint operators and relatively compact perturbations thereof. Prior to coming to Cambridge I did a BSc in Maths at Warwick. A copy of my CV can be found here.

My interests are fairly broad, but my research at the moment is on the interface between spectral theory and computability theory. Specifically, I am classifying the computational difficulty of certain problems – whether algorithms with certain properties exist solving a particular problem in a certain model of computation. So far I have particularly looked at spectral problems on Schrodinger operators, most recently the computation of spectral type.

Content on this blog will fall in three broad categories:

- Compilations of results that are hard to find with proof in literature, (or hard to find in one place, etc.) or cool results that are rarely covered in structured university study of a subject.
- Expositions about my own research, though original work will only appear after it is on arXiv. This will mean I won’t talk much about my work for a month or two yet.
- Tripos past paper solutions: I decided to start this blog the day before my Part III Functional Analysis exam in order to
~~procrastinate~~deposit typed solutions for most of Zsak’s past papers. I am open to writing solutions for other courses as well. Please drop me a line if this is something you and ideally some others are interested in before I sink a lot of time into it.

I can be reached by email at gc602 at cam dot ac dot uk. My PGP key can be found here.

### Research

- Provability and the Halting Problem (24/09/2024)

### Pages

- Part III Functional Analysis Past Paper Solutions (11/06/2023)
- Book recommendations (30/06/2024)
- Stuff I want to read (12/09/2024)