From partitions to Hodge numbers of Hilbert schemes of surfaces. (24th January 2020)

• Record Type: Journal Article
• Authors: Gillman, Nate; Gonzalez, Xavier; Ono, Ken; Rolen, Larry; Schoenbauer, Matthew
• Is Part Of: Philosophical transactions. Volume 378:Number 2163(2020)
• Publication Date: 2020-01-24
• Subjects: partitions -- Hilbert schemes -- Hodge numbers; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rsta.2018.0435
• Languages: English
• ISSNs: 1364-503X

Abstract

Abstract : We celebrate the 100th anniversary of Srinivasa Ramanujan's election as a Fellow of the Royal Society, which was largely based on his work with G. H. Hardy on the asymptotic properties of the partition function. After recalling this revolutionary work, marking the birth of the 'circle method', we present a contemporary example of its legacy in topology. We deduce the equidistribution of Hodge numbers for Hilbert schemes of suitable smooth projective surfaces. This article is part of a discussion meeting issue 'Srinivasa Ramanujan: in celebration of the centenary of his election as FRS'.