MSI Weekly Bulletin - Week starting Monday 7 November, 2005

We prove stability of rotationally symmetric translating solutions to mean curvature flow. Joint work with Felix Schulze and Oliver Schnürer.

As the first in a series of virtual seminars, we will be playing a videotaped lecture by Fields medallist Tim Gowers on 'The Importance of Mathematics'. A transcript is available at http:// www.dpmms.cam.ac.uk/~wtg10/importance.pdf and the video is kindly provided by the Clay Mathematics Institute.

Although parts of it border on combinatorics and probability theory, the theory of irregularities of point distribution began as a branch of the theory of uniform distribution, and may sometimes be described as a quantitative form of the theory. Uniform distribution originated from the remarkable paper of Hermann Weyl, in which he established the fundamental result known nowadays as the Weyl criterion. Weyl's work led to questions concerning the quality of the uniform distribution, and thus quantitative means to measure this quality. In this talk, following a brief introduction, we make use of the problem of discrepancy with respect to convex polygons to illustrate a few ideas in the subject, particularly on how diophantine approximation, probability theory and elementary geometry play important roles in some of the proofs. The talk will be self contained, and accessible to a general mathematical audience.