TITLE:  Discrete differentiation and local rigidity

ABSTRACT:

A Lipschitz function from the real line to itself is differentiable
almost everywhere.  In other words, a weak global regularity property
implies a strong local conclusion: At almost every point, the function
is locally well-approximated by its tangent line.  I will discuss how
suitable metric generalizations of this phenomenon have applications
to flows and cuts in graphs and the analysis of semi-definite
programs.