Title: Knotted Strings and Piecewise Isometric Dynamics
Directors: Noureen Khan, Byungik Kahng
Dates of Program: May 13 - August 3, 2013
This project is partly a continuation of the investigators' 2012 NREUP project, Links of Knot Theory in DNA Loops. It will expand the previous year's project somewhat further by offering an additional topic. The first topic, Knotted Strings, is a continuation from the previous year's project. It concerns the applications of knot theory to string theory in physics. The second topic, Piecewise Isometric Dynamics, touches the applications of discontinuous dynamics to digital signal processing in electric engineering. The investigators believe that it is possible to retain the depth of the research while expanding its breadth, because both topics share the common preparatory background, low dimensional topology, and therefore little additional time and effort will be needed to introduce the students to both topics.
Somewhat unexpected yet highly successful outcome of the investigators' 2012 project was the interaction with the high-school students in Texas Pre-freshman Engineering Program (TexPREP), supported by the state of Texas and UNT Dallas. The NREUP students got the practice presentation opportunities in UNT Dallas, ahead of the extramural presentations in conferences. Similar events will be duplicated this year, at or right after the conclusion of this project.
Student Researchers Supported by MAA:
Support for NREUP is provided by the National Science Foundation's Division of Mathematical Sciences and the National Security Agency.