Math Student Research Talks
Date: 3:30pm PDT October 4, 2018 Location: J.R. Howard Hall 259
J.R. Howard Hall 259
Geodesic Interpolation on Sierpinski Simplices
By Caitlin Davis - Mathematics Major
Interpolation between two sets can be viewed as the transport of mass between those sets. This concept is well understood in Euclidean space and on certain classes of manifolds. We study interpolation along geodesics in the Sierpinski simplices, a class of fractals which generalize the Sierpinski gasket to higher dimensions. The structure of these fractals allows for the existence of multiple geodesics between certain pairs of points. We prove a dimension-independent upper bound of eight on the number of geodesics between any two points. The structure of these fractals also results in the immediate collapse of the interpolant set to a one-dimensional set. We therefore study, rather than the size of the interpolant set, its “density.” We prove that, in the cases of cell-to-point and cell-to-cell interpolation, this density is self-similar with weights dependent on the dimension of the simplex.
The Math of Gerrymandering
By Sherlock Ortiz, Adriana Rogers and Anna Schall
(who are CS, CSMT and Math majors respectively)
Every 10 years when the U.S. Census occurs, Congress reapportions the number of seats that each state gets and the states redistrict accordingly. When that happens, parties can draw districts in ways that are most favorable to them, often marginalizing groups of people and making some votes count more than others. We researched how to make tools and metrics to help prove whether gerrymandering has occurred and to assess districts. Some of the tools and metrics we use are the Markov Chain Monte Carlo method, measuring compactness with Polsby Popper scores, and generating resources for expert witnesses to testify in gerrymandering cases.