We will talk about two problems: (a) that of finding good embeddings of finite metric spaces into L₁, the "Manhattan" metric and (b) finding cuts in graphs with small conductance. We will show that the two problems are closely related to each other, and how recent results for the former give us approximation algorithms for the latter.

As a corollary of our results, we show the following basic fact about metric

spaces: any n-point subset of L_1 can be embedded into Euclidean space so that the distances are distorted by a multiplicative factor of O(log^3/4 n), thus improving on a previous O(log n) bound of Bourgain (1986).

The talk is partly based on results with Shuchi Chawla and Harald Raecke, and will be self contained.