Advisor: Dr. James Wilson

Committee:  Dr. Alexander Hulpke, Dr. Dustin Tucker

Title: Decomposing bilinear maps

Abstract: Finding distinguishable communities in a large population, expressing groups as a direct sum of their subgroups, and determining the distinct sources of stress on a metal beam are all different versions of the same problem. The problem is how to uniquely decompose a set of data into smaller parts. To solve this problem, we can express our data as multilinear maps, also known as tensors. This question has been answered for the case of 3-tensors over finite rings, yet it remains unknown for infinite rings or tensors of valence greater than 3. I will present the tools used to decompose bilinear maps over finite rings, and I will present possible methods of extending these results to bilinear maps over infinite rings.