My research focuses primarily on topological invariants of knots, links and 3-manifolds. In particular, I am interested in various aspects of the Volume Conjecture. Some generalizations of the Volume Conjecture include severeal hypothetical relationships between geometric invariants, including Reidemeister torsions of 3-manifolds, and the leading and sub-leading terms in asymptotic expansions of certain quantum invariants, such as the partition functions of quantum Chern-Simons theories. In recent years, several new invariants of this kind have been constructed by the means of state integrals of Turaev-Viro type on triangulations of 3-manifolds. There is still a lot to be discovered about the asymptotic properties of such integrals.
Infinitesimal gluing equations and the
adjoint hyperbolic Reidemeister torsion,
preprint, to appear in the Tohoku Mathematical Journal.
Accompanying Sagemath script
- PhD Thesis: On the geometric meaning of the non-abelian Reidemeister torsion of cusped hyperbolic 3-manifolds, 2017
I rendered this visualization of an ideal tetrahedron in using Blender.