I will give a short introduction on the systematic construction of basis invariants in the 2HDM. Then I will discuss an application of this, namely testing for necessary and sufficient conditions for all symmetries of the 2HDM, including various CP transformations. There is an important overall lesson to be learned, namely that symmetries seem to be able to be classified into two cases, depending on how imposing them affects the basis invariants.
With support from FCT through project UIDB/00777/2020
