Explore the enigmatic world of Kronecker coefficients in this comprehensive lecture by Greta Panova at the Institute for Advanced Study. Delve into the multiplicities of irreducible Sn representations in tensor products of other irreducibles, introduced by Murnaghan in 1938. Discover how these coefficients generalize the Littlewood-Richardson coefficients of the General Linear group and their significance in Algebraic Combinatorics. Examine their role in Geometric Complexity theory and the quest for multiplicity obstructions in computational lower bounds for VP versus VNP. Gain insights into recent developments regarding positivity, asymptotics, and computational complexity of both Kronecker and reduced Kronecker coefficients. Learn about collaborative research findings with Christian Ikenmeyer, Igor Pak, and Damir Yeliussizov in this hour-long Special Year Seminar.