We are pleased to have Professor Yuval Peres, Theory Group, Microsoft Research, Redmond, as our honored speaker.
Thursday, October 5, 2017, at 4:30 PM, in Kent 120, 1028 E. 58th Street
Reception following the lecture in Jones 111, at 5:30 PM
ABSTRACT: Given uniform points on the surface of a two-dimensional sphere, how can we partition the sphere fairly among them? "Fairly" means that each region has the same area. It turns out that if the given points apply a two-dimensional gravity force to the rest of the sphere, then the basins of attraction for the resulting gradient flow yield such a partition-with exactly equal areas, no matter how the points are distributed. (See the cover of the AMS Notices at http://www.ams.org/publications/journals/notices/201705/rnoti-cvr1.pdf.) Our main result is that this partition minimizes, up to a bounded factor, the average distance between points in the same cell. I will also present an application to almost optimal matching of n uniform blue points to n uniform red points on the sphere, connecting to a classical result of Ajtai, Komlos and Tusnady (Combinatorica 1984).
Joint work with Nina Holden and Alex Zhai.