Geometry of Character Varieties (an ARC Discovery Project administered by Australian National University) (2025-2028)
Abstract
The aim of this project is to develop a comprehensive theory for the geometry of the spaces of symmetries called character varieties. The significance of these spaces stems from their central role in deep areas of mathematics and physics, such as the geometric Langlands program, mirror symmetry, and Yang--Mills theory. Expected outcomes include resolution of long-standing conjectures regarding invariants of character varieties. The benefits include applications in number theory and knot theory, and more broadly in cybersecurity, quantum computing, and economics. We will also strengthen the Australian mathematical research community by creating a hub in the southern hemisphere for the study of character varieties.
