# From partitions to Hodge numbers of Hilbert Schemes of Surfaces

## TL;DR

This paper explores the legacy of Ramanujan's work on partition functions by applying the circle method to demonstrate the equidistribution of Hodge numbers in Hilbert schemes of smooth projective surfaces.

## Contribution

It connects classical partition theory with modern topology, providing a new application of the circle method to geometric invariants.

## Key findings

- Hodge numbers are equidistributed in Hilbert schemes of certain surfaces
- The circle method is effectively applied in a topological context
- Historical connection between partition functions and geometric properties

## 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.