Georgia Institute of Technology College of Sciences

The hyperplane conjecture of Kannan, Lovasz and Simonovits asserts that the isoperimetric constant of a logconcave measure (minimum surface to volume ratio over all subsets of measure at most half) is approximated by a halfspace to within an absolute constant factor. I will describe the motivation, implications and some developments around the conjecture and an approach to resolving it (which does not seem entirely ridiculous).