
Abstract: I will present a geometric framework for EFTs that extends the notion of field-space covariance to include scalars, gauge bosons, and fermions. This approach simplifies both tree-level and quantum corrections by encoding amplitudes and one-loop divergences as geometric invariants of a field-space supermanifold. Using this formalism, we compute renormalization group equations for bosonic and fermionic operators in the SMEFT, including complete fermion-loop contributions up to dimension eight. I will also discuss a complementary EFT organization based on energy scaling and vertex structure, enabling a systematic identification of energy-enhanced operators at each order in the EFT expansion. This provides practical guidance for SMEFT analyses at the LHC and future colliders by isolating the operators most relevant for high-energy searches. Lastly, I will discuss a new proposal on EFT truncation uncertainty in the same vein as theory nuisance parameters in QCD which is needed but lacking in modern SMEFT searches.
