**Wednesday, March 7 – 3:30 pm — Room 380W**

** Fitting smooth functions to data:**

Let X be our favorite Banach space of continuous functions on R^n. Given a function f defined on some given subset of R^n, how can we decide whether f extends to a function F on all of R^n, belonging to the space X? If such an F exists, then how small can we take its norm?

What can we say about the derivatives of F at a given point? Can we take F to depend linearly on f?

Suppose E is a large finite set. Can we compute an F as above with norm having the least possible order of magnitude? How many computer operations does it take? What if we require only that F agree with f to a given accuracy, rather than demanding perfect agreement? What if we are allowed to discard a few data points as “outliers”? Which data points should we discard?

Joint work with Arie Israel, Bo’az Klartag, Kevin Luli and Pavel Shvartsman.

### Details

The Mathematics Research Center Distinguished Lecture Series Presents: Charles Fefferman (Princeton University)Charles Fefferman (Princeton University)

March 7, 2018

3:30 AM - 4:30 PM