Abstract: In this seminar I will first introduce you to heavy fermions and to the unsolved problem of the nature of the competition between Kondo screening and antiferromagnetic ordering in the heavy fermion quantum critical point. I will then present our investigation of this problem in the Kondo lattice model at half-filling in the Honeycomb lattice. I first present our 1/N renormalization group results. Then I discuss our recent ideas on going beyond the mean field theory of the Kondo-screening phase and consider destroying the Kondo coherence by proliferating Kondo vortex configurations. I finish by presenting our sign-free quantum Monte Carlo results for this model.