REU Site at UW Bothell

University Of Washington, Seattle WA

Investigators

Abstract

The REU site at UW Bothell will bring nine undergraduate students per summer to the University of Washington Bothell for a memorable research experience that will encourage and prepare them to pursue graduate education and research-oriented careers. Working closely with three faculty members on projects in knot theory, tiling theory, optimization, and biomedical analysis that are carefully chosen to be both accessible and significant, students will see firsthand that mathematical research can be both fun and interesting. The research experience will be complemented by professional development presentations, organized outings, and social activities. The investigators believe that this program will have a greater effect by recruiting students from underrepresented groups and from universities where research opportunities are limited; in particular, American Indians, women, and first generation college students from non-Ph.D. granting universities will be targeted. Each summer, the REU site will host three research groups consisting of three students and one faculty member. The research focus of the three groups will be from among the following four topics: Knot theory; interesting questions concerning lattice knots, in the standard cubic lattice as well as other lattices, such as the face-centered cubic lattice or the simple hexagonal lattice, will be pursued, including questions involving the minimal sized sphere that can contain a nontrivial knot (the sphere number of a lattice). Tiling theory; the problem of finding all convex pentagons that admit tilings of the plane is a long-standing unsolved problem. Students will develop an algorithm to search for pentagons that admit i-block transitive tilings of the plane, which could lead to the discovery of new convex pentagonal tiles that admit tilings of the plane. Optimization; Students will work to improve numerical optimization algorithms, including two variants of the modified spectral subgradient method. This project will also help develop students' scientific computing skills using MATLAB. Biomedical analysis; Students will develop methods for analyzing data from ultrasound devices used to detect abnormalities in brain tissue, including development of two-dimensional cross-correlation techniques to track ultrasound induced shear-wave propagation (whose speed is proportional to the shear modulus of tissue), development and testing of first principle models of that propagation as a function of material properties, and comparison of direct measures of brain-tissue stiffness.