Jayce Getz, Princeton Friday, Sept 12, 2008 Applications of the twisted relative trace formula to unitary groups The twisted relative trace formula was developed in order to apply results on periods of automorphic forms on general linear groups to the study of periods of automorphic forms on unitary groups. Periods on unitary groups are often related to algebraic cycles on Shimura varieties, so this provides an interesting link between automorphic representation theory and arithmetic geometry. We will discuss some illustrative examples.