Research

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.

Publications

• Infinitesimal gluing equations and the adjoint hyperbolic Reidemeister torsion, arXiv 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