Cluster Partition Function and Invariants of 3-Manifolds

The author reviews some recent developments in Chern-Simons theoryon a hyperbolic 3-manifold $M$ with complex gauge group $G$. Theauthor focuses on the case of $G=SL(N,mathbb{C})$ and $M$ being aknot complement: $M=S^{3}setminus mathcal{K}$. The main resultpresented in this note is the cluster partition function, acomputational tool that uses cluster algebra techniques to evaluatethe Chern-Simons path integral for $G=SL(N,mathbb{C})$. He alsoreviews various applications and open questions regarding thecluster partition function and some of its relation with stringtheory.