During the past two decades a surprising number of new structures have appeared in the geometric topology of low-dimensional manifolds influenced by physical theories. Their precise mathematical fomulation is often obtained by using non-commutative objects. For example, WRT invariants use the framework of quantum groups. The goal of this meeting is to discuss some topics where this interaction has led to new results, including gauge theory to string theory correspondence and conformal field theory and Khovanov homology.