# Group Compactifications and Moduli Spaces

## TL;DR

This paper explores how certain compactifications of split reductive groups can be understood as moduli spaces of framed bundles, extending to Artin stacks and discussing symplectic aspects for complex groups.

## Contribution

It provides a novel realization of toroidal compactifications as moduli spaces of framed bundles and extends the framework to Artin stacks with good moduli spaces.

## Key findings

- Toroidal compactifications realized as moduli spaces
- Extension to Artin stacks with good moduli spaces
- Discussion of symplectic counterparts for complex groups

## Abstract

We give a summary of joint work with Michael Thaddeus that realizes toroidal compactifcations of split reductive groups as moduli spaces of framed bundles on chains of rational curves. We include an extension of this work that covers Artin stacks with good moduli spaces. We discuss, for complex groups, the symplectic counterpart of these compactifications, and conclude with some open problems about the moduli problem concerned.