As an undergraduate researcher, I have participated in two separate summer research experiences:

University of Washington Bothell Mathematics REU
Hexagonal Knot Mosaics
Dr. Jennifer McLoud-Mann
Malachi Alexander
Selina Foster
Gianni Krakoff

The purpose of this research project is to develop a foundation of knot mosaic theory regarding the use of a hexagonal mosaic tile instead of the traditional square knot mosaic representations. In this project, we investigated the relevance of hexagonal knot mosaics and how these new representations are unique to their square counterparts. We hoped to find that these representations would in fact give a new take on the current knot mosaic theory and open the door to introducing a vast amount of new tile representations of knots. For more information about this research, click here!

Mathematical Sciences Research Institute Undergraduate Program
Topology of Positive Zero Sets of Bivariate Pentanomials
Dr. J. Maurice Rojas
Megan Ly
Malachi Alexander
Ashley De Luna
Christian McRoberts

The purpose of this research project is to automate the process of computing the topology of positive zero sets for n-variate (n+3)-nomials (n variables and n+3 terms) by developing an algorithm for the first unknown case: bivariate pentanomials. In our current work, we focus mainly on polynomials in the outer chambers of the A-discriminant variety and intend to extend this process to the inner chambers. For more information about this research, click here!