
The main area of my research interests is Low-Dimensional Topology. This basically means Topology of 3-Dimensional Manifolds and Knot Theory. The main problem of Low-Dimensional Topology is to classify the objects of study. Thus, I am very much interested in studying and trying to find new invariants of knots and 3-manifolds. In particular, I have been involved into studying new quantum invariants, such as Witten-Reshetihin-Turaev invariants, Turaev-Viro invariants, Murakami-Otsuki-Okada invariants, Dijkgraaf-Witten invariants, just to name few. Some of the questions that I have been tried to study are how these invariants reflect periodicity of 3-manifolds, to what extend can these invariants distinguish different 3-manifolds of a certain class (for instance, lens spaces), how these invariants are related to each other. I have also written computer programs for calculating some of the invariants. Another subject of my research is Skein Theory. I am trying to find useful algorithms for calculating skein modules of 3-manifolds and to apply those algorithms to certain manifolds.
