BPS cohomology for rank 2 degree 0 Higgs bundle

BPS cohomology for moduli spaces of Higgs bundles is a certain subspace of the compactly-supported cohomology of the stacks of semistable Higgs bundles that in some sense “generates” the full cohomology.
It is a conjecture of Davison that the BPS Lie algebra for degree 0 Higgs bundles on a genus g>1 is freely generated as a Lie algebra by the intersection cohomology of the coarse moduli spaces.  I will discuss the verification of this conjecture for the rank 2 part of the BPS Lie algebra, which follows from an analysis of the moduli stack of strictly semistable Higgs bundles that enables a comparison with the computation of the intersection cohomology of the coarse moduli space by Mauri.

In the pretalk I will motivate BPS cohomology by discussing simpler examples.