The International Research Fellowship Program enables U.S. scientists and engineers to conduct nine to twenty-four months of research abroad. The program's awards provide opportunities for joint research, and the use of unique or complementary facilities, expertise and experimental conditions abroad.
This award will support a twenty-four-month research fellowship by Dr. Carolyn B. Chun to work with Drs. Geoff Whittle and Dillon Mayhew at Victoria University in New Zealand.
A matroid is a structure that characterizes certain notions of independence in different fields in mathematics. Matroid theory abstracts these notions from linear algebra and graph theory to yield a more general combinatorial object. Matroid theory can also be seen as a study of the combinatorial properties of collections of points in space and has deep geometric and topological implications.
The most famous matroid conjecture that has not yet been solved concerns the matroids that can be represented by matrices with entries over a finite field, where a field is a set of numbers where arithmetic behaves as normal. The conjecture by Gian-Carlo Rota states that there are only finitely many minimal obstructions, known as excluded minors, to the class of matroids that may be represented by matrices with entries in any given finite field. Rota?s conjecture has been proved only in the cases when the fields have size two, three, or four. With Geoff Whittle and Dillon Mayhew, Carolyn Chun is making significant advances towards explicitly characterizing the excluded minors for representability over the five-element field. This work takes place in Wellington, New Zealand at Victoria University, which is widely regarded as one of the world's top centers for matroid research.
