Motivic degree 0 Donaldson-Thomas theory on a variety $X$ is a point counting theory on the Hilbert scheme of points on $X$ parametrizing zero-dimensionally supported quotient sheaves of $\mathcal{O}_X$. On the other hand, the high rank DT theory is about the so called punctual Quot scheme parametrizing zero-dimensional quotient sheaves of the vector bundle $\mathcal{O}_X^{\oplus r}$, while the unframed DT theory is about the stack of zero-dimensional coherent sheaves on $X$. I will talk about some recent progresses on explicit computations of these theories for singular curves $X$. For example, we found the exact count of $n\times n$ matrix solutions $AB=BA, A^2=B^3$ over a finite field (a problem corresponding to the motivic unframed DT theory for the curve $y^2=x^3$), and its generating function is a series appearing in the Rogers-Ramanujan identities. In other families of examples, it turns out that such computations discover new Rogers-Ramanujan type identities.