Cyclamen hederifolium and Coum, as seen in nature. I have also seen Muscari do well if not too shady.

the type of tree makes a difference - evergreens/conifers will, generally, mean that the base is always in shade but deciduous trees (those that lose their leaves in autumn) mean that spring bulbs could do well.

if the tree is recently planted then nothing until it is established. they will compete for water.
if established then depends on how much shade it produces. spring bulbs yep then things like ajuga, ferns, ivy, etc.