CV available on request, please email gc602 at cam dot ac dot uk. Please feel free to email this address with other questions or requests as well. I am considering roles in quantitative research, data science and machine learning.
Bio
I’m George, I am a third year CMI student supervised by Matthew Colbrook and Anders Hansen. Prior to coming to Cambridge I did a BSc in Maths at Warwick.
My interests are fairly broad, but my research lies on the interface between spectral theory and computability theory. We might have some physical system we can take measurements from or simulate, and we might ask whether it is possible to calculate a quantity associated with the system based off these measurements.
One would first have to translate this into a mathematical model, with the measurements perhaps becoming sample points and the goal becoming to compute the spectrum of an operator which these sample points identify. We then look to the Solvability Complexity Index, a rather recent construction which quantifies the computational difficulty of a certain problem. It transpires that, in many cases, the spectrum will be non-computable and hence this quantity will be unknowable or have a certain uncertainty attached to it. I work on establishing this kind of impossibility result for Schrodinger operators (which appear in mathematical physics) and Koopman operators (which appear in the study of nonlinear dynamical systems).
Outside of my research, I have (or have had) mathematical interests in Banach space theory, C*-algebras, convex optimisation, set theory, probability/stochastic calculus (doing both courses in Part III) and machine learning.
For those looking to read about Functional Analysis, I would highly recommend “Infinite Dimensional Analysis: A Hitchhiker’s Guide” (sounds general interest but is the most comprehensive Functional Analysis text going), Albiac/Kalton’s “Topics in Banach Space Theory”, Rudin’s Functional Analysis and Fabian et. al’s “Functional Analysis and Infinite-Dimensional Geometry”. The last text is excellent for about half of the Part III functional analysis course.
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 interesting 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.
- Tripos past paper solutions: I decided to start this blog the day before my Part III Functional Analysis exam in order to deposit typed solutions for most of Zsak’s past papers. I am open to writing solutions for other courses as well, drop me a line if you’d be interested.
Research
Currently rewriting most of these.
Pages
Part III Functional Analysis Past Paper Solutions (11/06/2023)