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Starting with the classical "Mahonian" combinatorial statistics inv and maj on permutations, this talk will demonstrate how these statistics naturally (or not-so-naturally) generalize to fillings of Young diagrams, which currently gives us the best understanding of the combinatorics behind the elusive Macdonald polynomials. The Macdonald polynomials are an important class of symmetric functions that naturally arise in many contexts, from probability theory to algebraic geometry. We will demonstrate how these Mahonian statistics can potentially provide new insight into the algebraic structures behind the Macdonald polynomials.