In this talk we will introduce an important theorem in representation theory that shows a surprising and deep connection between the representations of the general linear group and the representations of the symmetric group. Both groups act on the n-fold tensor product, but to figure out which irreducible representations appear in this space (and in particular with which multiplicity), one needs to study the simultaneous action of the two groups. Schur-Weyl Duality tells us that when one studies the action of the two groups, the decomposition of the n-fold tensor product into irreducible representations is actually multiplicity free. This talk will be accessible to graduate students of all years, but some familiarity with partitions and group algebras will be beneficial Speaker(s): Francesca Gandini (University of Michigan)