# From partitions to Hodge numbers of Hilbert schemes of surfaces

@article{Gillman2019FromPT, title={From partitions to Hodge numbers of Hilbert schemes of surfaces}, author={Nate Gillman and Xavier Gonzalez and Ken Ono and Larry Rolen and Matthew Schoenbauer}, journal={Philosophical Transactions of the Royal Society A}, year={2019}, volume={378} }

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…

## 6 Citations

### On the algebraicity about the Hodge numbers of the Hilbert schemes of algebraic surfaces

- MathematicsProceedings of the Edinburgh Mathematical Society
- 2022

Hilbert schemes are an object arising from geometry and are closely related to physics and modular forms. Recently, there have been investigations from number theorists about the Betti numbers and…

### Asymptotic equidistribution for partition statistics and topological invariants

- Mathematics
- 2021

We provide a general framework for proving asymptotic equidistribution, convexity, and logconcavity of coefficients of generating functions on arithmetic progressions. Our central tool is a variant…

### Distributions on partitions arising from Hilbert schemes and hook lengths

- MathematicsForum of Mathematics, Sigma
- 2022

Abstract Recent works at the interface of algebraic combinatorics, algebraic geometry, number theory and topology have provided new integer-valued invariants on integer partitions. It is natural to…

### Limiting Betti distributions of Hilbert schemes on n points

- MathematicsCanadian Mathematical Bulletin
- 2022

Hausel and Rodriguez-Villegas (2015, Astérisque 370, 113–156) recently observed that work of Göttsche, combined with a classical result of Erdös and Lehner on integer partitions, implies that the…

### The asymptotic profile of an eta-theta quotient related to entanglement entropy in string theory

- Mathematics
- 2019

In this paper we investigate a certain eta-theta quotient which appears in the partition function of entanglement entropy. Employing Wright’s circle method, we give its bivariate asymptotic profile.

### The asymptotic profile of an eta-theta quotient related to entanglement entropy in string theory

- MathematicsResearch in Number Theory
- 2020

In this paper we investigate a certain eta-theta quotient which appears in the partition function of entanglement entropy. Employing Wright’s circle method, we give its bivariate asymptotic profile.

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