**September 27, 2001 from
10:00-11:00 in K9509, SFU
**

**
**

** Adrian Lewis, SFU
Talks on
**

**"SMOOTHNESS AND SYMMETRY"
**

** Abstract:**
Consider a real even function f. Even though the Euclidean
norm |.| is not smooth at 0, the composite function
f(|.|) is differentiable if and only if f is. The same
is true for twice or three times differentiability, and
there are many analogous results (for example, for the
symmetric functions of matrix eigenvalues prevalent in
contemporary optimization). I will outline an
approach to these results via some multivariate
approximation theory used in the study of Sobolev spaces.