Title and abstract parts I and II

Integral currents are a natural generalization of oriented surfaces. The
concept was pioneered by De Giorgi for hypersurfaces of the
Euclidean space, and extended by Federer and Fleming to any
codimension, general Riemannian ambients, and different coefficient
groups. These classical works of the fifties and sixties established a
general existence theory for the problems of finding surfaces of least
area spanning a given contour and that of representing a fixed
homology class with area minimizers. On the other hand, at the onset
there are famous topological obstructions to the existence of smooth
solutions, but even in the absence of these obstructions, celebrated
examples show that minimizers are in general not smooth.
Even though I will mention the classical results for the hypersurfaces
case, in these lectures I will focus on the case of general codimension
and report on recent progress on the structure of singularities and on
the existence of smooth approximations.

October 16th and October 17th
4:30-5:30 p.m.
October 16th lecture will be held in 532 Malott Hall
October 17th lecture will be held in 406 Malott Hall
Refreshments will be served at 4:00 in 532 Malott prior to both talks.