2008 CSL Undergraduate Summer Research Stipends
Kok Ann "Sam" Gan | Scott Justus | Susan Mallgrave | Emily Mick | Christos Mitillos | Yacin Nadji | Angela Pak | Yaofu Zhou
Christos MitillosFourth-year undergraduate, Applied Mathematics and Computer Science Hemanshu KaulAssistant Professor of Applied Mathematics Open problems in graph theory |  | |
| Chris (left) will publish his original research. |
A 2007-2008 Project NExT Fellow, a professional development program for new or recent PhDs run by the Mathematical Association of America, Professor Kaul focuses on graph theory, combinatorics, discrete optimization, operations research, probabilistic models and methods in discrete mathematics. This summer, he worked with Chris on unsolved problems in graph theory.
"Graph theory is a way of describing binary relationships," said Kaul. A simple problem: to book classrooms for a semester, what is the least number of rooms needed without having a conflict? "Graph theory is the study of those relationships," he added. "It can be applied to problems involving thousands to millions of relationships that occur in both social and physical sciences."
All summer, Chris worked on problems involving "fall chromatic number of graphs," a combination of graph coloring and dominating sets. "Graph coloring" is a partition of graph vertices into color classes. The partition is a "proper coloring" if no two related vertices are in the same color class. A "dominating set" is the fewest number of vertices from which all vertices in a graph can be reached within a step. "For example, consider the locations for a communications network or emergency services like fire stations. You'd want to reach all of the vertices as quickly as possible," said Kaul. In fall chromatic number of graph problems, Chris sought insight into how both could be used.
Chris will publish his work, a step toward his goal of earning a PhD in discrete mathematics and becoming a professor. A double major, Chris has placed in both ACM programming and MAA mathematics competitions and was a mathematics Olympiad in his native Cyprus. Like many students preparing for graduate school, he welcomed the opportunity to do original research.
"A PhD is not about coursework or homework," noted Kaul. "It's, 'Here's a question we don't have an answer for' — and you try to find that answer. It's more creative."
Photographer: Mindy Sherman, IIT Communications & Marketing
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