# UBC Mathematics Colloquium

## Bill Minicozzi

(Johns Hopkins University, USA)

## Generic singularities of mean curvature flow

### Fri., Oct. 2, 2009, 3:00pm, MATX 1100

In mean curvature flow (or MCF), a surface evolves to minimize its
surface area as quickly as possible. One of the challenges of MCF
is that the flow starting from a closed surface (like a sphere) always
becomes singular and one of the most important problems is
understanding these singularities. The simplest example comes
from a round sphere, which evolves by staying round but having the
radius shrink until it hits zero and then just disappears. Matt
Grayson proved that this is the only type of singularity that occurs
for simple closed curves in the plane. However, many other
examples were discovered in higher dimensions (most of them by applied
mathematicians doing numerical simulations). I will describe
recent work with Toby Colding, MIT, where we classified the generic
singularities of MCF of closed embedded hypersurfaces. The thrust
of our result is that, in all dimensions, every singularity other than
shrinking spheres and cylinders can be perturbed away.