Abstract:We will consider a many-body problem, where the non-relativistic bosons are interacting with each other through the two-body Dirac delta potential on two dimensional manifolds. This problem leads to an unphysical conclusion that its ground state energy is unbounded from below. One way to solve this issue is to renormalize the model. We will give a non-perturbative renormalization method for this model, which is first proposed by Rajeev in flat case. We will then apply mean field approximation in the large number of particle limit to estimate the ground state energy of the system. (Joint work with Teoman Turgut).