Speaker
Description
In the paper De Concini, C.; Lusztig, G.; Procesi, C. Homology of the zero-set of a nilpotent vector field on a flag manifold. J. Amer. Math. Soc. 1 (1988), no. 1, 15-34, it was proven the so-called Springer fiber $B_n$ for any nilpotent n element in a complex simple Lie algebra $g$ has homological properties that suggest that $B_n$ should have a paving by affine spaces. This last statement was proved to hold in the case in which $g$ is classical but remained open for exceptional groups in types $E_7$ and $E_8$. In a joint project with Maffei we are trying to fill this gap. At this point our efforts has been successful in type $E_7$ and "almost" in type $E_8$ where one is reduced to show it only in one case.
The goal of the talk is to survey the problem and give an idea on how to show our new results.
