In this talk, we discuss nearly G2 structures, which define positive Einstein metrics, and are, up to scale, critical points of a geometric flow called (modified) Laplacian co-flow. We will discuss a recent joint work with Jason Lotay showing that many of these nearly G2 critical points are unstable for the flow. 

In this talk I will describe a possible strategy to obtain new solution to LMCF in the Kummer K3 surface by a fixed point argument. The key idea is that the regions where curvature concentrates in the Kummer K3 surface are modeled on the Eguchi-Hanson space. 

Temperley-Lieb algebras are certain finite-dimensional algebras coming originally from statistical physics and knot theory. Around 2019, they became one of the first examples of homological stability for algebras (homology is here taken to be certain Tor-groups), when Boyd and Hepworth showed that in low dimensions the homology vanishes. We're now able to give complete calculations of their homology, which has a surprisingly rich structure (and in particular is very far from vanishing). This is joint work in progress with Rachael Boyd, Oscar Randal-Williams, and Robin Sroka. Prerequisites will be minimal: it will be enough to know what Tor is.