  The intersection of electronic topology and strong correlations offers a rich
platform to discover exotic quantum phases of matter and unusual materials. An
overarching challenge that impedes the discovery is how to diagnose topology in
strongly correlated settings, as exemplified by Mott insulators. Here, we
develop a general framework to address this outstanding question and illustrate
its power in the case of Mott insulators. The concept of Green's function Berry
curvature -- which is frequency dependent -- is introduced. We apply this
notion in a system that contains symmetry-protected nodes in its noninteracting
bandstructure; strong correlations drive the system into a Mott insulating
state, creating contours in frequency-momentum space where the Green's function
vanishes. The Green's function Berry flux of such zeros is found to be
quantized, and is as such direct probe of the system's topology. Our framework
allows for a comprehensive search of strongly correlated topological materials
with Green's function topology.
