Abstract

 ABSTRACT: I will discuss rigidity (existence or nonexistence of

infinitesimal deformations) and stability (strict local minimization)

properties of Einstein metrics for quadratic curvature functionals on

Riemannian manifolds. This is joint work with Matt Gursky.

Details

This is a meeting of instructors from UBC and Vancouver high schools. The purpose of the meeting is to discuss issues of transition from high school to university, particularly in the context of mathematics.An agenda of speakers and panels may be found at
   www.math.ubc.ca/~fsl/meeting.html

Abstract

Consider the Poisson point process in Euclidean space. We are interested in functions on this random point set whose value in each configuration point is given by some ``local" rule (no ``central planning"). One example is the so-called allocation problem,
where we want to partition $\R^d$ to sets of volume 1 and match them with the point process, in a translation equivariant way. We want to make the allocated set optimal in some sense (e.g., the distribution of the diameter shows fast decay). We will present some allocation schemes, among them one with an optimal tail, which is our recent construction with R. Marko.