Frank and Brennie Morgan Prize Citations and Responses

The Frank and Brennie Morgan Prize recognizes and encourages outstanding mathematical research by undergraduate students. Undergraduates are working on problems of current research interest, proving theorems, writing up results for publication, and giving talks on their work. There is undergraduate research today at the highest standards of professional excellence. The prize was endowed by Mrs. Frank Morgan and also carries the name of her late husband.

Citation
Joshua Greene

The winner of the 2002 Morgan Prize for Outstanding Research by an Undergraduate is Joshua Greene for his work in combinatorics. His prize is based on his paper "A new short proof of Kneser's conjecture" which is to appear in the American Mathematical Monthly, and his undergraduate senior thesis "Kneser's conjecture and its generalizations".

Discrete mathematics has often been enriched by the interplay of topology and combinatorics. One such example is Lovász classic 1978 proof of Kneser's conjecture which states that if the k-element subsets of a n-element set are partitioned into n-2k+1 classes then one of the classes must contain a pair of disjoint subsets. Greene gave a beautiful new short proof without using Gale's theorem on the distribution of points on a sphere. His proof is a gem that is widely admired and has already been included in a forthcoming book by Matousek. In his senior thesis, Greene addresses further associated combinatorial questions and has already provided two new simplified proofs of Schrijver's theorem on chromatic-critical subgraphs of Kneser graphs. His insight in topological combinatorics bypasses traditional technical difficulties in this area, and experts predict that his method will become the standard approach in this rapidly developing area of mathematics.

The committee was impressed by the depth and quality of Greene's research, and by his command of a large body of topology, geometry and combinatorics required for his work. The quality of his research papers, the enthusiastic letters from his mentors, and the response to his work from many researchers all confirm the outstanding nature of his research.

The committee is proud to award the 2002 Frank and Brennie Morgan prize to Joshua Greene.

Biographical Notes

Josh Greene was born and raised in the sprawling suburbs of Columbia, Maryland. After early unsuccessful attempts to become an artist and pro hockey player, Josh took up an interest in science and mathematics during high school. Beginning in his junior year, he studied astrophysics under the guidance of Dr. Jay Norris at NASA / Goddard Space Flight Center, and was named a Finalist in the 1998 Westinghouse Science Talent Search for his work there. In the summer of 1998, Josh was a student at the Hampshire College Summer Studies in Mathematics, which sparked his interest in combinatorics, and he returned to teach at the program in 1999 and 2002. He matriculated at Harvey Mudd College in 1998, where he enjoyed a broad education and learning from a dedicated, enthusiastic faculty, graduated with distinction in mathematics in 2002. During college, Josh also participated in the Budapest Semesters in Mathematics, Joseph Gallian's Research Experience for Undergraduates in Duluth, Minnesota, and the Director's Summer Program. Each program uniquely shaped his research experience and current interests, which include discrete mathematics, number theory, and topology. Josh is currently building houses with Habitat for Humanity in Appalachia through the Americorps service program, and he plans to enter the University of Chicago next fall to pursue a doctorate in mathematics. When he is not studying or communicating mathematics, Josh enjoys hockey, Frisbee, nature, and trying to determine the meaning of life.

Response from Joshua Greene

I am deeply honored by this distinction. My sincerest thanks extend to Mrs. Frank Morgan for endowing this prize, and to the AMS, MAA, and SIAM for sponsoring it and awarding it to me this year. I owe this honor to everyone who has contributed to my research experience in college. Amongst these many people, I specifically thank Joseph Gallian for supervising my work at the Duluth REU; to Liz Pyle, for overseeing my work at the Director's Summer Program; to András Gyárfás, whose combinatorics course inspired a substantial portion of my research; to Art Benjamin, Weiqing Gu, and Mike Moody, for their ongoing support; and, moreover, to my advisor Francis Su, for his tireless encouragement and guidance in all matters mathematical and otherwise. Finally, I thank my friends, Kate, and my family for all of their tremendous support.