Talk 1 Title: The current smallest linearization model for the quadratic assignment problem Abstract: It is well known that Kaufmann-Broeckx linearization is the current smallest linearization for the quadratic assignment problem. Whether it is the exact smallest one is open. In this talk, we give a negative answer to this open question by constructing a smaller linearization model. Talk 2 Title: A new lower bound via a new projection for the quadratic assignment problem Abstract: In this talk, based on a new projection formulation, we deduce a new promising lower bound for the quadratic assignment probme.