Random Partitions, Hurwitz Numbers and Counting High Genus Surfaces
Explore a 47-minute conference talk presented by Harriet Walsh from the Université d'Angers at IPAM's Integrability and Algebraic Combinatorics Workshop. Delve into the fascinating world of random partitions, Hurwitz numbers, and high genus surface counting. Discover how Frobenius' formula allows for the interpretation of unconnected Hurwitz numbers as normalization factors for probability laws on integer partitions, known as Plancherel-Hurwitz measures. Examine the asymptotic behavior of random partitions under these measures in a regime where normalization factors count unconnected surfaces of high genus. Gain insights into estimating high genus unconnected Hurwitz numbers and consider questions about random unconnected surfaces and bijective interpretations of Frobenius' formula. Based on joint work with Guillaume Chapuy and Baptiste Louf, this talk offers a probabilistic approach to understanding complex mathematical concepts in combinatorics and surface topology.