# Wild character varieties, meromorphic Hitchin systems and Dynkin diagrams

## TL;DR

This paper explores the extension of Hitchin systems to wild character varieties, aiming to classify these complex geometric objects using Dynkin diagrams, thereby advancing the understanding of non-compact cases.

## Contribution

It introduces a framework for classifying wild character varieties and proposes a Dynkin diagram-based approach for their systematic study.

## Key findings

- Development of a classification scheme for wild character varieties
- Extension of Hitchin system theory to non-compact cases
- Proposal of Dynkin diagrams as a tool for classification

## Abstract

The theory of Hitchin systems is something like a "global theory of Lie groups", where one works over a Riemann surface rather than just at a point. We'll describe how one can take this analogy a few steps further by attempting to make precise the class of rich geometric objects that appear in this story (including the non-compact case), and discuss their classification, outlining a theory of "Dynkin diagrams" as a step towards classifying some examples of such objects.