in studying complex chern-simons theory on a seifert manifold, gukov-pei proposed an equivariant verlinde formula, a one-parameter deformation of the celebrated verlinde formula. it computes, among many things, the graded dimension of the space of holomorphic sections of (powers of) a natural determinant line bundle over the hitchin moduli space. gukov-pei conjectured that the equivariant verlinde numbers are equal to the equivariant quantum k-invariants of a non-compact (kahler) quotient space studied by hanany-tong. in this talk, i will explain the setup of this conjecture and its proof via wall-crossing of moduli spaces of (parabolic) bradlow-higgs triples. it is based on work in progress with wei gu and du pei.