Constructing solutions to arbitrary diffusion processes using higher geometry and maximum calibre

I gave the following seminar at UCL’s Theoretical Neurobiology meeting.

Abstract:

How can we construct solutions to arbitrary diffusion processes? This question poses a challenge, as diffusion processes can be characterised as (non-linear, chaotic) partial differential equations. As such, this is effectively a subset of a large, open problem in analysis and mathematical physics, which is a general treatment of the theory of PDEs. We will use strategies from the former in pursuit of this objective, namely, formalisms from higher geometry for defining arbitrary dynamics in a space. From this, we derive an adaptation of Jaynes’ Maximum Calibre, offering a principled construction of a general solution to diffusion-based PDEs. We further examine how to apply these results in data-driven calculations.

Talk: link to recording

Slides: TNB March 2021.pdf

Amended post hoc with notes: TNB March 2021 (amended).pdf