Midwest Algebra, Geometry and their Interactions Conference MAGIC05 University of Notre Dame, Notre Dame October 7-11, 2005 Free resolution of square-free monomial ideals by Tai HA, Tulane University Abstract: This talk will discuss a new combinatorial approach to studying the minimal free resolution of square-free monomial ideals. I will concentrate on the class of quadratic square-free monomial ideals, which can be viewed as edge ideals of graphs. The method also extends quite successfully to an arbitrary square-free monomial ideal viewed as the facet ideal of a simplicial complex.