Implicit construction of polynomials by symmetrization of Young tableaux

Recently several conjectures were resolved by using a classical method for constructing vectors in irreducible representations of coordinate rings of group varieties. We explain the method and several applications, for example a proof of Weintraub's 1990 conjecture on plethysm coefficients (with Bürgisser and Christandl) and a disproof of Mulmuley and Sohoni's 2008 occurrence obstruction conjecture in geometric complexity theory (with Bürgisser and Panova). Moreover, we explain how we were able to shed more light on several other conjectures by running the method on cluster computers.