Behrend number and blowups of planar fat points

In this seminar, I will talk about the Behrend function of fat points of the affine plane. This invariant was defined by Kai Behrend in 2009 and it is considered a powerful tool in enumerative geometry. In general, calculating the Behrend function is a hard task. As a consequence, this function is known only for very few examples. During the seminar I will show some methods for the computation of the Behrend function of fat points with embedding dimension 2 and, if time permits, I will show some difficulties in generalizing these results to higher dimension. A key tool in the computation will be the blowup of fat points in the affine plane. The talk is based on an article I wrote with Andrea T. Ricolfi (SISSA): "On the Behrend function and the blowup of some fat points" (Advances in Mathematics 415)