Odd systems, characterised by broken time-reversal or parity symmetry, 
exhibit striking transport phenomena due to transverse responses. In this 
talk, I will introduce the concept of odd diffusion, a generalisation of 
diffusion in two-dimensional systems that incorporates antisymmetric tensor 
components. Focusing on systems of interacting particles, I adapt a 
geometric approach to derive effective transport equations and show how 
interactions give rise to unusual transport in odd systems. I present 
effects like enhanced self-diffusion, reversed Hall drift and even absolute 
negative mobility that solely originate in odd diffusion. These results 
reveal how microscopic symmetry-breaking gives rise to emergent, equilibrium 
and non-equilibrium transport, with implications for soft matter, chiral 
active systems, and topological materials.

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.