**Title:** Non-uniquely ergodic interval exchange transformations

**Abstract:** Starting from rotations of the circle and flows on flat tori the I’ll discuss the dynamics of interval exchange transformations and flows on flat surfaces. Rotations have the remarkable property that if a rotation has a dense orbit then every orbit is uniformly distributed. This fails for interval exchange transformations and I’ll discuss some of behavior that these examples can exhibit and some results on the size of this exceptional set.