Location: Olin 305
When: February 22nd at 1:30 p.m.
Title: A Bayesian view of geometry
Abstract: The embedding problem for Riemannian manifolds was solved by Nash in the 1950s. Since the 1960s, this work has been seen as a fertile source of techniques in geometry and PDE. In the past decade, these theorems have reappeared unexpectedly in several apparently unrelated scientific contexts, in particular machine learning and turbulence, stimulating a renewed investigation of Nash’s work.
I will describe a new framework for the analysis of the embedding theorems that is based on information theory. This framework builds on the embedding-turbulence analogy to provide new algorithms, new models and new theorems for many applications. The foundation is a probabilistic characterization of the isometric embedding problem obtained with Dominik Inauen (Leipzig).
A general theme is the manner in which the analysis of PDE of continuum mechanics, perhaps our most traditional models in physics, can be enhanced and challenged by the use of Bayesian methods.
Zoom link: https://wse.zoom.us/j/94601022340