Costello Yamazaki and Witten have proposed a new understanding of quantum integrable systems coming from a variant of Chern-Simons theory living on a product of two Riemann surfaces. I’ll review their work, and show how it can be extended to the case of integrable systems with boundary. The boundary Yang-Baxter Equations, twisted Yangians and Sklyanin determinants all have natural interpretations in terms of line operators in the theory.

Finding Riemannian metrics with holonomy G_2 is a challenging problem with links in mathematics to Einstein metrics and area-minimizing submanifolds, and to M-theory in theoretical physics.  I will provide a brief survey on recent progress towards studying this problem using a geometric flow approach, including connections to calibrated fibrations.

Snapshot mosaic multispectral imagery acquires an undersampled data cube by acquiring a single spectral measurement per spatial pixel. Sensors which acquire p frequencies, therefore, suffer from severe 1/p undersampling of the full data cube.  We show that the missing entries can be accurately imputed using non-convex techniques from sparse approximation and matrix completion initialised with traditional demosaicing algorithms.

I will discuss Agol's proof of the Virtually Fibred Conjecture of
Thurston, focusing on the role played by the `RFRS' property. I will
then show how one can modify parts of Agol's proof by replacing some
topological considerations with a group theoretic statement about
virtual fibring of RFRS groups.