The canonical seesaw models are one of the simplest and most natural scenarios that can account simultaneously for neutrino masses and matter-antimatter asymmetry in our universe. Below the seesaw scale, one can integrate out the heavy degrees of freedom to construct the seesaw effective field theory (SEFT). In this talk, we investigate the connection between the full seesaw model and the low-energy SEFT from a brand-new perspective: the invariant theory. Using the powerful tool of Hilbert series, we demonstrate the intimate relation between the flavor space of the SEFT and that of its ultraviolet theory. Through the matching of flavor invariants, it is revealed that the precise measurements of dimension-five and dimension-six operators in the SEFT at low energies are powerful enough to probe the full seesaw model, including CP violation necessary for successful leptogenesis.