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.