13:15
Ricci flow on ALF manifolds
Abstract
Asymptotically Locally Flat (ALF) Ricci-flat metrics are expected to model certain long-time singularities in four-dimensional Ricci flow, so understanding their stability is essential. In this talk, I will discuss that conformally Kähler, non-hyperkähler Ricci-flat ALF metrics are dynamically unstable under Ricci flow. Our work establishes three key tools in this setting: a Fredholm theory for the Laplacian on ALF metrics, the preservation of the ALF structure along the Ricci flow, and an extension of Perelman’s λ-functional to ALF metrics. This is joint work with Tristan Ozuch.
Last year BBC Breakfast launched a puzzle advent calendar in collaboration with GCHQ. It was a huge hit and so they want to follow it up a bi-weekly challenge (probably Monday and Friday) in the Spring, set by a panel of experts/quizzers. They are "are hoping to recruit around a dozen of the best minds in the country to help set these challenges", in this case female minds for gender balance.