# The cohomology rings of the unordered configuration spaces of the torus

## TL;DR

This paper investigates the cohomology ring of unordered configuration spaces on the torus, computing its mixed Hodge structure, mapping class group action, and establishing formality over the rationals.

## Contribution

It provides explicit computations of the cohomology ring, mixed Hodge structure, and demonstrates formality, advancing understanding of configuration spaces on the torus.

## Key findings

- Computed the cohomology ring structure
- Determined the mixed Hodge structure
- Proved formality over the rationals

## Abstract

We study the cohomology ring of the configuration space of unordered points in the two dimensional torus. In particular, we compute the mixed Hodge structure on the cohomology, the action of the mapping class group, the structure of the cohomology ring and we prove the formality over the rationals.