Title: Closed Mean Curvature Flows with Prescribed Tangent Flows

Abstract: We show that every nonflat smooth embedded shrinker that is closed, smoothly asymptotically conical, or a product of such a shrinker with a Euclidean factor can arise as a multiplicity-one tangent flow at the first singularity of a mean curvature flow starting from a closed embedded hypersurface. We also discuss how certain first-order asymptotics near the singularity can be prescribed. This is joint work with Jingwen Chen, Tang-Kai Lee, and Ao Sun.

Title: Isoperimetry by stretching 

Abstract: Isoperimetric boundaries minimise area for fixed enclosed volumes, with sharp regularity theory ensuring they are smooth away from a closed singular set of codimension seven. I will discuss recent work, with G. Niu, which constructs isoperimetric regions from hypersurfaces in closed manifolds. As a direct application, we show that a wide variety of topological types and singular sets arise in isoperimetric boundaries.

Title: 

Abstract: 

Title: 

Abstract: 

Title: 

Abstract: 

Title: On a construction of hermitian metrics on holomorphic vector bundles

Abstract: With any holomorphic vector bundle E over a compact base one can associate a certain line bundle L (often denoted O_{PE}(1)). According to a conjecture of Griffiths from the 1960s, if L admits a positively curved hermitian metric k, then E also admits a positively curved hermitian metric, h. In the talk I will discuss recent developments on this, in particular, a refutation of the conjecture.

Title: 

Abstract: 

Title: 

Abstract: 

Title: 

Abstract: 

Title: 

Abstract: 

Title: 

Abstract: 

Title: 

Abstract: 

Title: 

Abstract: 

Title: 

Abstract: 

Title: 

Abstract: