San Diego State University Mathematics Research Experience for Undergraduates

2015 Project: Arithmetic of Matrix Semigroups

Factorization theory is the study of the fundamental elements of an algebraic structure and the ways in which these fundamental elements can be combined to describe all elements of the structure; eg. all positive integers can be represented uniquely as a product of prime integers. We will consider the factorization theory of noncommutative semigroups, with the specific goal of computing invariants that measure the uniqueness or non-uniqueness of factorizations in certain semigroups of matrices.

Program Director: Vadim Ponomarenko
Dr. Ponomarenko has been directing undergraduate and REU research for 15 years. Most REU participants he has worked with have been coauthors on at least one paper as a result of this collaboration.
Program co-Director: Christopher O'Neill
Christopher O'Neill is a PostDoc at Texas A&M University, and has several years of experience with undergraduate research and factorization theory. In addition to the SDSU Math REU program, he has worked with the Pacific Undergraduate Research Experience in Mathematics.

Technical Consultant: Nicholas Baeth
Dr. Nicholas Baeth teaches at the University of Central Missouri and recently held a research/teaching Fulbright award in Austria. Dr. Baeth has worked with dozens of undergraduate and masters students on research projects. Nearly all of these projects involved some aspect of factorization theory, and most have led to publications co-authored with his students.

Projects from previous years: 2007, 2008, 2009, 2012, 2013, 2014