For a given finite p-group P where p is a prime, one can ask such as; Can
we know all finite groups G with a Sylow p-subgroup P? As a kind of
generalization of this, in modular representation theory of finite groups
there is a famous conjecture, called "Donovan's conjecture" due to Peter
Donovan, which says that for a given finite p-group P there should be (up
to Morita equivalence) only finitely many block algebras B of finite
groups such that P is isomorphic to defect groups of B. We will be
discussing mainly one particular interesting case of wild representation
type such that for this case even a bit stronger conjecture called "Puig's
conjecture" due to Llouis Puig does hold. This is joint work with Caroline
Lassueur and Benjamin Sambale.