Title:  Terraces, Latin squares, and the Oberwolfach problem

Abstract:  A terrace is an arrangement of the elements of a finite group in which differences between adjacent elements adhere to certain restrictions. We introduce terraces and a number of related objects, including R-terraces and directed terraces, and discuss conjectures concerning the groups for which we can construct terraces. We also consider applications of terraces to problems in the areas of combinatorial design and graph theory - namely, the construction of row-complete Latin squares and solutions to some particular cases of the Oberwolfach problem.