Higher rank motivic Donaldson-Thomas invariants of $\mathbb{A}^3$ via wall-crossing, and asymptotics

Abstract

We compute, via motivic wall-crossing, the generating function of virtual motives of the Quot scheme of points on $\mathbb{A}^3$, generalising to higher rank a result of Behrend, Bryan and Szendr\H{o}i. We show that this motivic partition function converges to a Gaussian distribution, extending a result of Morrison.