Villanova, Pa – Permutations are ways to describe symmetries and arrangements of objects. They have applications in many fields, including computer science, where they are used in sorting algorithms; physics, where they are utilized to describe states of quantum particles; and biology, where they are employed to describe ribonucleic acid sequences.
Alexander Diaz-Lopez, PhD, associate professor, Mathematics and Statistics in Villanova University’s College of Liberal Arts and Sciences, has been named principal investigator on a two-year, $249,937 National Sciences Foundation Launching Early-Career Academic Pathways in the Mathematical and Physical Sciences grant. The grant will support Dr. Diaz-Lopez’s project, “Combinatorics from an Algebraic and Geometric Lens,” which will study permutations from a combinatorial and geometric point of view.
Dr. Diaz-Lopez’s research interests are in algebra and combinatorics. This project seeks to describe the composition of permutations that share a given collection of properties and their spatial distribution when plotting these permutations in a Cartesian space. The second focus of the project is the study of arithmetical structures of graphs. Finally, the project will serve to create the Villanova-Puerto Rico Research Retreat, a collaboration research summer program between students at Villanova University and the University of Puerto Rico.
“The grant will not only support my research, but also the research of Villanova students during the academic year, and students from both Villanova and the University of Puerto Rico—my undergraduate alma mater—during the summer,” says Dr. Diaz-Lopez, who is a native of Puerto Rico. “It will also help expand a student research symposium for our Mathematics and Statistics students and fund students’ travel to national conferences.”
In 2021, Dr. Diaz-Lopez received a Henry L. Alder Award for Distinguished Teaching from the Mathematical Association of America. This national award recognizes faculty whose teaching has been extraordinarily successful and whose effectiveness in teaching mathematics is shown to have influence beyond their own classrooms. In addition, Dr. Diaz-Lopez is active in graduate teaching and mentoring at the University and has been instrumental in developing programs that prepare underrepresented students for graduate school.
Dr. Diaz-Lopez received his doctorate from the University of Notre Dame.
About Villanova University’s College of Liberal Arts and Sciences: Since its founding in 1842, Villanova University’s College of Liberal Arts and Sciences has cultivated knowledge, understanding and intellectual courage for a purposeful life in a challenging and changing world. With more than 40 majors across the humanities, social sciences and natural sciences, it is the oldest and largest of Villanova’s colleges, serving more than 4,500 undergraduate and graduate students each year. The College is committed to a teacher-scholar model, offering outstanding undergraduate and graduate research opportunities and a rigorous core curriculum that prepares students to become critical thinkers, strong communicators and ethical leaders with a truly global perspective.