Ethan Coldren, 2017 Goldwater Honorable Mention

The summer after high school, Ethan attended the CoCoA 15 combinatorics conference, which sparked an even greater interest in combinatorics. Fascinated, he enrolled in MATH 502, graduate level Combinatorics II, and then MATH 501, Combinatorics I.

To further his knowledge, Ethan sought an independent study with my MATH 501 professor. This past summer, he conducted research at the University of Michigan in information theory, generalizing the Blahut-Arimoto algorithm for computing rate-distortion and channel capacity. This summer, he will be doing research under Dr. Florian Frick at Cornell University studying the intersection of topology and combinatorics.

Ethan has also been working with Dr. Kate Ross and Dr. Marty Gelfand in the physics department, writing a Python program to compute the ground state spin configuration of a magnetically frustrated crystal. He is enjoying the opportunity to learn more about numerical analysis and to conduct research combining this area of math with my knowledge of physics and computer science.

Additionally, he is helping the Society of Physics Students club to construct a spark chamber; he has computed how many cosmic rays they will observe for various dimensions, to determine what size of spark chamber they'll want to build. Ethan is also involved with the design of the high-voltage circuit and purchasing of components for it.

Early in his freshman year, Ethan began an independent study with Dr. Ross McConnell, an algorithmic graph theorist, and that spring he took his CS 520, Analysis of Algorithms graduate class.

Since that time, Ethan has worked as a teacher's aide for his CS 320 class, Algorithms-Theory and Practice and participated in several of Dr. McConnell's research groups, studying various subclasses of perfect graphs and some certifying algorithms to recognize them, in addition to solving some normally NP-complete problems, like coloring, independent set, and maximum clique in polynomial time.

This semester, he is completing another independent study with Dr. McConnell to cover circular arc graphs, and a paper that was recently posted on the ArXiV detailing a O(n4) certifying algorithm for recognizing circular arc graphs. Although a linear time certifying algorithm for the "yes" case has been published, the best for the "no" case is O(n4), and Dr.McConnell, one of his Ph.D. candidates, and Ethan is working to find a faster algorithm.