Geometric aspects of symmetric tensor decompositions

Kristian Ranestad (Oslo)

I will introduce apolarity as a tool to investigate decompositions, and discuss various notions of rank defined in terms of polarity. Important topics in this discussion are artinian Gorenstein rings and arithmetic Gorenstein varieties. The second part of the lectures will be devoted to varieties of decompositions. I shall present both classical and more recently discovered power sum varieties. Throughout the students will be challenged to work on a variety of examples.