Self-introduction: Christy Kelly
Hi, I'm Christy Kelly. I studied physics for my undergraduate degree in London before moving to Edinburgh to do a PhD in theoretical physics at Heriot-Watt university, completed in early 2022. I have now joined iTHEMS as an SPDR. I am interested in gravity, especially coarse aspects of gravity that persist in the absence of differentiable structure; in more physical terms, we can perhaps think of this as gravity in regimes where quantum fluctuations become significant. In such regimes, basic mathematical tools such as calculus are no longer valid and it becomes nontrivial how to characterise even such fundamental notions as curvature. To get around this problem, I hope to exploit the recently flourishing mathematical field of optimal transport theory, which has already become a paradigm for the study of low regularity Riemannian geometry and has seen some very exciting recent developments in the Lorentzian case. Unexpected connections to different fields of physics also arise naturally in the optimal transport theoretic framework: for instance, the Einstein equations can be characterised in terms of the convexity/concavity properties of certain entropy functionals along choice trajectories in spacetime. Optimal transport theory also provides a notion of curvature for networks which has proved of some structural significance; I hope to also take this line of research forward during my time here at iTHEMS.