Paul Villanueva

Predictive Plant Phenomics Trainee - 2017 cohort
Graduate Research Assistant
Paul Villanueva

I received my BS in Mathematics at California State University, Long Beach, where I was named the Mathematics and Statistics 2017 Outstanding Baccalaureate Graduate. My studies emphasized theoretical mathematics and included graduate-level courses in knot theory, algebra, and real analysis. I also have a minor in computer science with an emphasis on algorithm analysis. Besides taking a graduate-level course in the subject, I led discussion sections for data structures and discrete math for several semesters and was a lab assistant in a motion capture-based research study.

In my senior year, I received an NSF grant through the National Math Alliance to work with Dr. Ryan Blair on defining the Wirtinger number of a knot. The Wirtinger number is a novel definition of bridge number based on the minimal number of generators needed to generate the Wirtinger presentation of the fundamental group of the knot exterior over all equivalent representations. I wrote an algorithm to calculate the Wirtinger number and have used it to tabulate the bridge numbers of approximately 50,000 prime knots with up to 14 crossings that were previously unlisted. This information is available at Charles Livingston's Table of Knot Invariants.

Area of Expertise: 
Bioinformatics and Computational Biology
B.S., Mathematics, California State University - Long Beach, 2017
0079 Roy J. Carver Co-Laboratory, 1111 WOI Road