In this talk, I will introduce a systematic approach to computing the BPS spectra of any 5d/6d supersymmetric quantum field theory in Coulomb phases, which admits either gauge theory descriptions or geometric descriptions, based on the Nakajima-Yoshioka’s blowup equations. The blowup formula will be generalized in terms of both properly quantized magnetic fluxes on the blowup C2 and the effective prepotential for 5d/6d field theories on the Omega background which is uniquely determined by the Chern-Simons couplings on their Coulomb branches. This allows us to compute BPS spectra of all rank-1 and rank-2 5d Kaluza-Klein (KK) theories descending from 6d N=(1,0) superconformal field theories (SCFTs) compactified on a circle with/without twist.
