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Macdonald polynomials meet Mahonian statistics

Student-Run Applied & Math Seminar

Speaker: Maria Monks, UC Berkeley
Location: 2112 MSB
Start time: Wed, Apr 30 2014, 1:10PM

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.