A quandle is an algebraic system with a binary operation satisfying three axioms that are algebraic formulations of the three Reidemeister moves of planar diagrams of links in the 3-space. The talk starts with definition and some examples of quandle. In this talk, we will define residual finiteness properties on quandles and discuss their implications. We will prove that the fundamental n-quandle of any link in the 3-sphere is residually finite for each n ≥ 2. This supplements the recent result on residual finiteness of link quandles and the classification of links whose fundamental n-quandles are finite for some n. If time permits, we also discuss several general results on these finiteness properties and many families of quandles admitting them.

Dr Neeraj Kumar Dhanwani is a postdoctoral fellow in Mathematics at IISER Mohali. He has earned a PhD in Mathematics from IISER Bhopal. His area of research is broadly Geometry and Topology. In particular, he works on mapping class groups of surfaces and quandles.

All are welcome