Midwest Algebra, Geometry and their Interactions Conference MAGIC05 University of Notre Dame, Notre Dame October 7-11, 2005 Linkage and Gorenstein linkage by Bernd ULRICH, Purdue University Abstract: In this talk we are going to report on joint work with Robin Hartshorne and Craig Huneke and with Craig Huneke, respectively. The topic are ideals in the linkage class of a complete intersection (called licci ideals) and ideals in the Gorenstein linkage class of a complete intersection (called glicci ideals). Most notably we prove that any residual intersection of a licci ideal is glicci. We also show that zero-dimensional monomial ideals are glicci, and we give an algorithmic criterion for such an ideal to be licci.