The talk is about the hyperrigidity of operator systems. Despite being disproven by Bilich and Dor-On, Arveson’s hyperrigidity conjecture remains open in the case of operator systems in commutative C*-algebras. We will present new results on the hyperrigidity of the operator system given by the continuous affine functions on compact convex subsets in R^2. Additionally, we present a finite-dimensional operator system in a noncommutative C*-algebra that contradicts Arveson’s conjecture.   Note: the seminar will be completely virtual - only in zoom.