Gluon structure of hadrons and nuclei from lattice QCD

The construction of an electron-ion collider (EIC) designed to reveal new information about the gluon structure of hadrons and nuclei is planned, with data taking expected within the next decade. I will describe recent lattice QCD studies of the gluon generalised form factors of both hadrons and light nuclei, motivated by providing Standard Model predictions for quantities to be measured for the first time at the future EIC. I will focus in particular on the transversity gluon structure quantities which are of interest since they are purely gluonic and do not mix with quark distributions. In light nuclei these quantities moreover provide a clean signature of non-nucleonic gluon degrees of freedom, which have not yet been observed experimentally but are cleanly resolved in the lattice calculations.