Abstract: Let C be a very general complex smooth projective algebraic curve endowed with a
groupof automorphisms G such that the quotient C/G has genus at least 3. I will show
thatthe algebra of Q-endomorphisms of the Jacobian J(C) of C is naturally isomorphic to
thegroup algebra QG. Time permitting, I will then explain some applications of this result
tothe theory of virtual linear representations of the mapping class group. This talk is based
on a joint work with Eduard Looijenga (cf. arXiv:1811.09741).