# Local curves, wild character varieties, and degenerations

## TL;DR

This paper proposes conjectural formulas for cohomological invariants of wild character varieties by counting curves in degenerate Calabi-Yau threefolds, connecting Gromov-Witten theory with wild character variety invariants.

## Contribution

It introduces new conjectural formulas linking curve counting in degenerate Calabi-Yau threefolds to wild character variety invariants, extending previous results.

## Key findings

- Conjectural formulas for E-polynomials of wild character varieties.
- A refined conjecture generalizing existing Poincaré polynomial results.
- Connections established between Gromov-Witten theory and wild character invariants.

## Abstract

Conjectural results for cohomological invariants of wild character varieties are obtained by counting curves in degenerate Calabi-Yau threefolds. A conjectural formula for E-polynomials is derived from the Gromov-Witten theory of local Calabi-Yau threefolds with normal crossing singularities. A refinement is also conjectured, generalizing existing results of Hausel, Mereb and Wong as well as recent joint work of Donagi, Pantev and the author for weighted Poincar\'e polynomials of wild character varieties.