Rafał M. Siejakowski

Instituto de Matemática e Estatística
Universidade de São Paulo

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


I rendered this visualization of an ideal tetrahedron in using Blender.