Sami Al-Asaad

Given a projective variety X, one can construct a geometric object that parametrizes the endomorphisms of X, known as the endomorphism scheme, of which the set of connected components has a natural algebraic structure of a monoid. In this talk, I introduce some finiteness results concerning such monoids of connected components (for example, the maximal subgroups are all bounded), highlighting some basic connections with the geometry of X. The talk requires basic knowledge of algebra, and will hopefully be accessible to everyone.