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<p align="center"><img src="interests.gif" width="500" height="50" alt="My Research Interests"></p>
<p>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. </p>
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