Quantum invariants and hyperbolic manifolds in three-dimensional topology

The Project aims to broaden our understanding of three-dimensional spaces, including spaces that arise in
engineering, microbiology and physics.
It is known that all three-dimensional spaces can be decomposed into geometric pieces. The most common type
of geometry is hyperbolic. It is also known that such spaces have algebraic structures arising from quantum
physics, known as quantum invariants. Several important conjectures, based on developments in physics, assert
that hyperbolic geometry and quantum invariants are deeply related, but they remain unproved.
The Project aims to find new relationships between hyperbolic geometry and quantum invariants, advancing our
understanding of both areas.