Evolving Syllabus
4-9-2007: Brief History of GMT with stories; A recent result as motivation; An overview of a few ideas from GMT -- conceptual snapshots.
4-16-2007: "Normal and Rectifiable Currents", Part 1; Why currents and varifolds?; what are currents and varifolds?; n-vectors, n-covectors, n-forms; boundaries.
4-23-2007: "Normal and Rectifiable Currents", Part 2 : addendum to last lecture; Mass; compactness; representation by integration; a zoo of currents;
4-30-2007: We jump back to Lipschitz maps, rectifiable sets, the area and coarea formulas, a brief mention of Marstrand's and Preiss' theorems and then ahead to minimal surfaces and isoperimetric inequalities.
5-7-2007: We will start with two addendums -- one on mean curvature and stationary surfaces and one on calibrations. Then we will cover products of currents, push forward of a current.
5-14-2007: Homotopy Formula, Cones, Deformation theorem: an initial look.
5-21-2007: Deformation theorem, Isoperimetric Inequality, compactness and existence of area-minimizing surfaces.
5-28-2007: National Holiday (Memorial Day)
6-4-2007: Motivation for Densities, Properties of Densities, Rectifiable sets have approximate tangents almost everywhere