# Mathematics Colloquium

#### Fair Allocations to Random Points

**Speaker:**
Ron Peled, Courant Institute of Mathematical Sciences, NYU

**Location:**
Warren Weaver Hall 1302

**Date:**
Monday, November 2, 2009, 3:45 p.m.

**Synopsis:**

Given an infinite collection of points in space, how do we allocate the same area to each point in a decentralized, shift‐invariant way? Such allocations have been the subject of many investigations in recent years and different approaches to the problem have used such tools as: the Gale‐Shapley stable marriage algorithm, the Riemann mapping theorem and Newtonian gravity. I will survey results in the field, with special focus on the Gradient Flow Allocation, a natural allocation rule suggested by Sodin and Tsirelson, and its variant ‐ the Gravitational Allocation. My own contribution to the subject is joint with Sourav Chatterjee, Yuval Peres and Dan Romik.