Christopher Cornwell: Augmentations in knot contact homology and SL(2,C) character varieties

We will discuss some recent results on obtaining information about the SL(2,C) charater variety of the double branched cover over a knot from augmentations of the DGA of its unit conormal lift. We will also discuss some applications, such as determining when a knot complement has a simple SU(2) character variety (which is of interest for singular instanton knot homology) and when the fundamental group of the double branched cover has a left-invariant order (which is relevant to a conjecture of Boyer-Gordon-Watson).