Cats, mathematicians, and low-dimensional topology, with PIMS PDF Nicholas Rouse at UBC.

I specialize in low-dimensional topology, focusing on hyperbolic 3-manifolds, which are both plentiful and rigid, unlike in other dimensions. In dimension 3 and higher, hyperbolic manifolds play a central role, while in dimension 2, there is a large Teichmüller space worth of hyperbolic structures on most manifolds. The Geometrization Theorem states that 3-manifolds can be decomposed into geometric pieces, of which hyperbolic geometry is the most interesting and least understood. My work aims to extract geometric information from number-theoretic invariants resulting from rigidity. Specifically, I study the behavior of these invariants under certain operations, such as cutting along a disk and gluing together copies of what remains. The picture below illustrates this operation. <a href="https://medium.com/pims-math/cats-mathematicians-and-low-dimensional-topology-with-pims-pdf-nicholas-rouse-at-ubc-105fb7d07166">Click Here</a>