Soheyla Feyzbakhsh (Imperial): Rank r DT theory from rank 1

Fix a Calabi-Yau 3-fold X satisfying the Bogomolov-Gieseker conjecture of Bayer-Macrì-Toda, such as the quintic 3-fold. I will explain joint works in progress with Richard Thomas that aim to express Joyce’s generalised DT invariants counting Gieseker semistable sheaves of any rank r on X in terms of those counting sheaves of rank 1. By the MNOP conjecture, the latter are determined by the Gromov-Witten invariants of X. Our technique is to use wall-crossing with respect to weak Bridgeland stability conditions on X.