A major modern problem in topological string theory is the studying of instanton moduli spaces, and their associated partition functions. We will try to explain the mathematical counterpart of this problem (Donaldson-Thomas theory), which allows to properly study (in many interesting cases) the geometry of these moduli spaces and to express the partition functions as a statistical weight of box arrangements. The focus will be given on how to operatively perform computations, of interest on the physics side, without prior deep understanding of the underlying physical models. This a report on joint works with Y. Cao, M. Kool, N. Fasola and A. Ricolfi. 

https://indico.math.cnrs.fr/event/11345/