After successful completion of the course, students are able to know the basic theory of currents, as well as the most important measure-theoretical results, and open problems, and will be able to hold a short-presentation about the topic.

Mathematical currents are, roughly speaking, distributions acting on the space of differential forms. They were originally introduced in order to solve Plateau's problem and are nowadays a powerful tool to generalize the notion of oriented submanifold in a measure-theoretical way. After reviewing basic notions of measure theory and differential forms, we will discuss the motivation for the introduction of currents, as well as their main properties and applications.

The first presentations will be held by E. Davoli and E. Tasso, in order to recall some preliminary results and introduce basic theoretical concepts. All participants will then take turns in presenting at the blackboard some assigned material.

The first meeting will be organizational and will take place on March 5th at 11:00 in DA06G14 (Freihaus, 6th floor, Green).

Active participation and seminar presentations.