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Explore the intricacies of counting set partitions by genus in this 49-minute lecture by Jean-Bernard Zuber from the Institut des Hautes Etudes Scientifiques (IHES). Delve into the revisited approach to partition counting, starting with the well-known case of genus 0 (non-crossing partitions). Learn how a functional equation between generating functions allows for the reconstruction of all partitions from the "(semi)-primitive" ones introduced by Cori and Hetyei. Examine explicit examples in genus 1 and 2, and if time permits, review known results and conjectures about higher genus. Reference two relevant papers for further study: Zuber's work on counting partitions by genus (genus 0 to 2) and a compendium of results co-authored with Robert Coquereaux.
