  Brain rhythms emerge as a result of synchronization among interconnected
spiking neurons. Key properties of such rhythms can be gleaned from the
phase-resetting curve (PRC). Inferring the macroscopic PRC and developing a
systematic phase reduction theory for emerging rhythms remains an outstanding
theoretical challenge. Here we present a practical theoretical framework to
compute the PRC of generic spiking networks with emergent collective
oscillations. To do so, we adopt a refractory density approach where neurons
are described by the time since their last action potential. In the
thermodynamic limit, the network dynamics are captured by a continuity equation
known as the refractory density equation. We develop an appropriate adjoint
method for this equation which in turn gives a semi-analytical expression of
the infinitesimal PRC. We confirm the validity of our framework for specific
examples of neural networks. Our theoretical findings highlight the
relationship between key biological properties at the individual neuron scale
and the macroscopic oscillatory properties assessed by the PRC.
