Some Open Questions in Quiver Gauge Theory

TL;DR

This paper presents a collection of open research questions at the intersection of quiver gauge theories, representation theory, and algebraic geometry, aiming to guide future investigations in these interconnected fields.

Contribution

It compiles and discusses recent open questions in quiver gauge theories, highlighting their relevance across mathematics and physics and suggesting directions for future research.

Findings

Identifies key open problems in gauge theories and algebraic geometry.

Connects supersymmetric gauge theories with representation theory.

Provides a research roadmap for PhD-level investigations.

Abstract

Quivers, gauge theories and singular geometries are of great interest in both mathematics and physics. In this note, we collect a few open questions which have arisen in various recent works at the intersection between gauge theories, representation theory, and algebraic geometry. The questions originate from the study of supersymmetric gauge theories in different dimensions with different supersymmetries. Although these constitute merely the tip of a vast iceberg, we hope this guide can give a hint of possible directions in future research. This is an invited contribution to a special volume of Proyecciones, E. Gasparim, Ed., and it is the hope that the questions are specific enough for research projects aimed at PhD students.