Computing Diffusion Geometry

Date

Nov 6, 2025

Time

3:00 PM - 4:00 PM

Speaker

Iolo Jones

Affiliation

Durham University

Language

en

Main Topic

Biologie

Host

Local Organisers: Nikola Sadovek, Maximilian Wiesmann, Giulio Zucal

Description

Calculus and geometry are ubiquitous in the theoretical modelling of scientific phenomena, but have historically been very challenging to apply directly to real data as statistics. Diffusion geometry is a new theory that reformulates classical calculus and geometry in terms of a diffusion process, allowing these theories to generalise beyond manifolds and be computed from data. In this talk, I will describe a new, simple computational framework for diffusion geometry that substantially broadens its practical scope and improves its precision, robustness to noise, and computational complexity. We introduce a range of new computational methods, including all the standard objects from vector calculus and Riemannian geometry, spatial PDEs and vector field flows, and topological features like cohomology, circular coordinates, and Morse theory. These methods are fully data-driven, parameter-free, scalable, and can be computed in near-linear time and space.

Last modified: Nov 6, 2025, 7:40:03 AM