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AMS-MAA-SIAM Frank and Brennie Morgan Prize for Outstanding Research in Mathematics by an Undergraduate Student

The new Frank and Brennie Morgan Prize stands dergraduate at the to recognize and encourage outstanding math- University of Michi- ematical research by undergraduate students. gan, he had been Undergraduates are working on problems of pursuing a program current research interest, proving theorems, of research in ana- writing up results for publication, and giving lytic number theory talks on their work. There is undergraduate re- and has made out- search today at the highest standards of pro- standing contribu- fessional excellence. The prize was endowed by tions to that field. Mrs. Frank Morgan and also carries the name of A year ago he her late husband. (Their son, Frank Morgan of solved a long-stand- ing and much stud- Williams College, is on the prize selection com- ied conjecture of mittee.) Kannan Soundararajan Ron Graham, jointly The first Frank and Brennie Morgan Prize was with R. Balasubra- awarded at the Joint Meetings in Orlando in Jan- manian. When at Bell Labs two years ago, he es- Kannan Soundararajan uary 1996 to of tablished asymptotic formulae for the distribu- Princeton University. An Honorable Mention was tion of “smooth polynomials”. Especially in the awarded to Kiran Kedlaya of Harvard Univer- last two undergraduate years he has had great sity. The prize selection committee consisted of success in establishing properties of the Rie- Kelly J. Black, Gulbank D. Chakerian, Frank mann zeta function on the line Rs =1/2. His Morgan, Robert Robson, John Ryff, Martha Siegel work has brought him acclaim from accom- (chair), Gilbert Strang, and Lee Zia. plished researchers in the field, who have cited Kannan Soundararajan him as a superb analytic number theorist. His work involves estimates of (1/2+it) and es- Citation timates for the gaps between| the zeros| of the Kannan Soundararajan (Sound) has presented zeta functional. The work that the committee a body of truly exceptional research. As an un- found most compelling was the sophisticated

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approach to the spacing of the ordinates of the planar partitions of planar graphs has brought zeros of the zeta function. Scholars in the field acclaim from experts, who emphasize that he has claim that his results have completely rewritten made more progress than many professionals the subject. He has already had four papers ap- who have tackled it. Although only a few infinite pear in outstanding research journals, has had families of vertex-transitive non-Cayley graphs two other papers accepted, and has submitted are known, Kiran has added another. He also has three others. obtained several new results and new proofs of Response known results in the area of solving constrained I take great pleasure in accepting this award. Pell equations. Over the last few years I have had the pleasant Biographical Sketch and rewarding experience of interacting with Kiran Kedlaya hails from Silver Spring, MD, many notable mathematicians. For sharing their and is currently a senior at Harvard University mathematical wisdom, their infectious enthusi- studying mathematics and physics. He plans to asm for the subject, and their patient indul- get a Ph.D. and probably enter academia. His in- gence, I gladly thank them all. In particular I am terest in mathematics was piqued in high school grateful to Professors R. Balasubramanian, by such activities as the American Regions Math A. Granville, H. L. Montgomery, K. Ramchandra, League (ARML) competition and the American and T. D. Wooley, who remain constant sources Mathematical Competitions (AMC). He was a of encouragement. three-time winner of the USA Math Olympiad and attended the International Math Olympiad three Biographical Sketch times (winning two gold medals and one silver Sound was born in Madras and spent most of medal). Since graduating from high school, he has his high school years there. He studied at the continued his involvement with the AMC, writ- Padma Seshadri High School, whose teachers, he ing questions for the USAMO and assisting in the claims, were responsible for stimulating his in- Math Olympiad Summer Program. He is also a terest in mathematics. They suggested that he two-time Putnam Fellow. visit the Institute for Mathematical Sciences, Kiran was recommended to the Morgan Prize which is one of the centers for mathematical re- Committee by Joe Gallian, who knew his work search in Madras. There he came in contact with from his participation in the REU at the Univer- Professor R. Balasubramanian, to whom Sound sity of Minnesota, Duluth. Kiran’s mathematical owes his interest in number theory. Faculty mem- interests include algebraic number theory, al- bers at the University of Michigan, where Sound gebraic geometry, and combinatorics. His non- was an undergraduate and a member of the mathematical interests include volunteering with 1993 fifth-ranked Putnam team, recommended the American Red Cross; singing in the Harvard him to the Morgan Prize Committee. Sound Glee Club; playing chess, bridge, and ultimate placed seventh in the Putnam Competition in frisbee; and learning foreign languages. 1994. He is now a graduate student in mathe- matics at Princeton University. Apart from math- ematics he is quite fond of literature, music, and chess. He says that he hopes that someday he will play Go without blushing.

Honorable Mention

Kiran Kedlaya Citation Much of Kiran’s research has been carried out in connection with summer research or in- ternship programs for undergraduates. He has an impressive portfolio of four professional- level research papers that demonstrate sophis- tication, depth, and versatility far beyond what might be expected of a student due to graduate in June 1996. He has substantially improved on results of Babai and Sós (1985) on the size of the largest product-free subset of a finite group of order n. The referee’s report on the paper calls it “lovely” and continues with, “The elementary combinatorial idea is quite ingenious.” Kiran’s progress on a tough problem involving outer-

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