Tue, 17 Feb 2026
13:15
C4

Ricci flow on ALF manifolds

Dain Kim
(MIT)
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.

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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. 

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PhDYourWay are running a free online webinar, entitled "Is a Maths PhD Right for Me?", sponsored by the London Mathematical Society Inclusion and Diversity Fund, and the Institute of Mathematics and its applications. 

If a PhD seems mysterious, overwhelming, or just plain confusing, this is your chance to get the inside scoop from people who are living it right now. Join a one-hour live Q&A with current Mathematics PhD students from across the UK, who will share their insights about:

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