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Learn about a groundbreaking mathematical research presentation exploring the intersection of Igusa zeta functions, combinatorics, and poset topology through a 30-minute lecture delivered at the ESI Workshop on "Recent Perspectives on Non-crossing Partitions through Algebra, Combinatorics, and Probability." Discover how the development of a novel polynomial, which refines Maglione-Voll's rational expressions, the Poincaré polynomial of hyperplane arrangements, and the ab-index of posets, led to proving significant conjectures about pole numbers and multiplicities. Explore how findings initially focused on geometric lattices extend to noncrossing partition lattices, representing collaborative work between Dorpalen-Barry, Joshua Malione, and Christian Stump at the Erwin Schrödinger International Institute for Mathematics and Physics.
