# Graduate Student / Postdoc Seminar

#### Discretization and Affine Approximation in High Dimensions

Speaker: Sean Li

Location: Warren Weaver Hall 1302

Date: Friday, April 20, 2012, 1 p.m.

Synopsis:

Bates, Johnson, Lindenstrauss, Preiss, and Schechtman proved that Lipschitz maps from the unit ball of a finite dimensional space into a superreflexive Banach space must be approximately affine on some smaller ball of a controlled radius r. However, one cannot read any kind of estimate of r from their proof. We present a new proof that gives a concrete lower bound for r. We also apply the affine approximation estimate to reprove Bourgain's discretization theorem for a restricted case and give a background to the related Ribe program.