Title: Singularities of generic mean curvature flows
Abstract: Surfaces evolving by mean curvature flow in R3 can develop rather complicated singularities. However, it was conjectured by Huisken that generically only very simple singularities can form. This conjecture was recently resolved by works of Chodosh-Choi-Mantoulidis-Schulze and Bamler-Kleiner. I will discuss these results, as well as what more we can say.
Professor Szekelyhidi is given a special lecture on some of the introductory materials at 12:30 the same day in the department. All are welcome to attend both talks.
Short Bio: Gábor Székelyhidi is a professor at Northwestern University, and he received his PhD in 2006 from Imperial College London.
His research deals with geometric analysis and complex differential geometry, including the existence of canonical metrics on projective manifolds, and the relations between extremal metrics and K-stability for polarised varieties and especially Fano varieties.
In 2014 he was an invited speaker at the International Congress of Mathematicians in Seoul. He was elected as a Fellow of the American Mathematical Society in the 2024 class of fellows.