Mathematics

In this talk I will describe how one can observe q-Virasoro constraints for the partition functions of 3d supersymmetric theories. I will start with the brief review of the usual Virasoroconstraints in the Hermitian matrix model and their constructionthrough the free boson representation. Then I will generalize these well known constructions to the case of q-Virasoro algebra. Finally I will explain physical meaning of this generalization in terms of the partition functions of 3d theories.