From partitions to Hodge numbers of Hilbert schemes of surfaces-Reference-Cited by-同舟云学术

From partitions to Hodge numbers of Hilbert schemes of surfaces

Published:2019-12-09 Issue:2163 Volume:378 Page:20180435
ISSN:1364-503X
Container-title:Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Phil. Trans. R. Soc. A.

Author:

Gillman Nate¹,Gonzalez Xavier²,Ono Ken³^ORCID,Rolen Larry⁴,Schoenbauer Matthew⁵^ORCID

Affiliation:

1. Department of Mathematics and Computer Science, Wesleyan University, Middletown, CT 06457, USA

2. Mathematical Institute, University of Oxford, Oxford, UK

3. Department of Mathematics, University of Virginia, Charlottesville, VA 22904, USA

4. Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA

5. Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, USA

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’.

Funder

National Science Foundation

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2018.0435

Reference19 articles.

1. Congruence properties of partitions;Ramanujan S;Proc. London Math. Soc.,1919

2. Addition and counting: the arithmetic of partitions;Ahlgren S;Not. Am. Math. Soc.,2001

3. Asymptotic Formulaae in Combinatory Analysis