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2003 Morgan Prize 2003 Morgan Prize The 2003 AMS-MAA-SIAM and the awardee’s response upon receiving the Frank and Brennie Morgan prize. The same information is provided for the Prize for Outstanding Research honorable mention. in Mathematics by an Undergraduate Student was Melanie Wood awarded at the Joint Citation Mathematics Meetings in The winner of the 2003 Morgan Prize for Out- Phoenix in January 2004. standing Research by an Undergraduate is Melanie The Morgan Prize is Wood. The award is based on research on two dif- awarded annually for out- ferent topics: Belyi-extending maps and P-orderings. standing research in mathe- The first topic is concerned with finite coverings matics by an undergraduate student (or students having of the projective line that are ramified only at three submitted joint work). Stu- points of the projective line. The absolute Galois dents in Canada, Mexico, or group of the field of rational numbers acts on the United States or its pos- these coverings and on diagrams (that Grothendieck Melanie Wood sessions are eligible for con- named dessins d’enfants) associated with the cov- sideration for the prize. Es- erings. Melanie Wood’s research gives a way to tablished in 1995, the prize was endowed by Mrs. generate genuinely new Galois invariants of dessins Frank Morgan and carries the name of her late hus- from old ones. Her work yields important insights band. The prize is given jointly by the AMS, the into the actions of the Galois group on funda- Mathematical Association of America (MAA), and mental groups. This research has attracted the the Society for Industrial and Applied Mathemat- attention and admiration of the specialists work- ics (SIAM) and carries a cash award of $1,000. ing in this field. The paper has been submitted for Recipients of the Morgan Prize are chosen by a publication. joint AMS-MAA-SIAM selection committee. For the In a separate project, Melanie Wood studies 2003 prize the members of the selection committee P-orderings in Dedekind rings. These P-orderings were: Kelly J. Black, Fan Chung Graham, Thomas C. were introduced by Bhargava in 1995 to generalize Hales (chair), Svetlana R. Katok, Kris Stewart, and the usual factorial function. It is well known that a Philippe M. Tondeur. polynomial with rational coefficients takes integer Previous recipients of the Morgan Prize are: Kan- values at the integers if and only if it is an integer nan Soundararajan (1995), Manjul Bhargava (1996), linear combination of binomial coefficient polyno- Jade Vinson (1997), Daniel Biss (1998), Sean mials xCk . One of her results in this area implies McLaughlin (1999), Jacob Lurie (2000), Ciprian that, in imaginary quadratic fields, the integer-valued Manolescu (2001), and Joshua Greene (2002). polynomials cannot possess a basis of this same The 2003 Morgan Prize was awarded to MELANIE general form. Melanie began this work during the WOOD. Receiving an honorable mention was KAREN 2000 Duluth Summer Research Program (directed YEATS. The text that follows presents the selection by Joseph Gallian), and her paper on P-orderings has committee’s citation, a brief biographical sketch, recently appeared in the Journal of Number Theory. 438 NOTICES OF THE AMS VOLUME 51, NUMBER 4 Richard Hain (with help from Makoto Matsumoto) has proved a multiplicative version for Dirichlet mentored her work at Duke. series of a classical estimate of Schur on the size of Melanie Wood’s research has been described in the coefficients of a product of two power series. glowing terms by her mentors and by other experts In her second paper Yeats determines bounds in her field. The work is deep and original. The com- on the size of values of a character, expressed as a mittee commends her for the mature mathemati- function of the degree of the character, for excep- cal perspective in her writings. The AMS, the MAA, tional compact Lie groups. This research completes and SIAM are pleased to award the 2003 Frank and the work of other researchers, who had previously Brennie Morgan Prize to Melanie Wood. obtained results for classical compact Lie groups. Biographical Sketch In a third paper she makes a model-theoretic Melanie Wood graduated from Duke University in investigation of exotic identities of the positive May 2003 with highest distinction in mathematics. integers. An exotic identity is one involving addition, Her math competition honors include top place multiplication, and exponentiation that is not a finishes in the USA Mathematical Olympiad and the consequence of eleven basic arithmetic identities, Asian Pacific Mathematical Olympiad, and the articulated by Dedekind in 1888. designation of Putnam Fellow. She won both a The committee was impressed by the quality of the Gates Cambridge Scholarship and a Fulbright to papers, the enthusiastic letters from her mentors, study at the University of Cambridge, where she is and the speed and independence of her research. currently doing a one-year math program. This fall The committee is proud to honor Karen Yeats with she will enter the math Ph.D. program at Princeton this award. on a National Science Foundation Graduate Fel- Biographical Sketch lowship. Her current research interests are in Karen Yeats is a native of Halifax, NS, Canada. She algebraic number theory and arithmetic algebraic began enjoying mathematics through regional, geometry. Melanie also enjoys acting, especially national (Canadian), and foreign contests. She classical acting and voice work; directing; danc- entered the University of Waterloo in September ing; and philosophy. 1998 and graduated with an honors BMath in Pure Response Math and a Governor General’s Silver Medal in I am extremely honored to be awarded this prize. 2003. During that time she had the opportunity to My experiences doing math research have been spend three summers as an NSERC (Natural Sci- tremendously rewarding and the critical factor in ences and Engineering Research Council of Canada) my decision to continue on to graduate work in undergraduate research assistant and benefited mathematics. That I had these experiences at all is greatly from the strong faculty and program in due to two institutions that enable and encourage pure mathematics at Waterloo. She is now pursu- undergraduate math research: Duke University and ing a Ph.D. in mathematics at Boston University. the REU [Research Experiences for Undergraduates] Karen is an accomplished recorder player and also at the University of Minnesota, Duluth. At Duke, I enjoys playing clarinet and singing in choirs, as well wish to thank Richard Hain, who supervised my as the occasional foray into making teddy animals research on the absolute Galois group, and Robert and working on free software. Bryant, who was available for many helpful con- Response versations. I wish to thank Makoto Matsumoto for I am truly honored to have been named honorable quick and helpful responses to technical questions. mention for this year’s Morgan Prize. Great thanks I also wish to thank Joe Gallian, director of the to the creators and organizers to whom the prize Duluth REU, for his support of my research, and all owes its existence. I also owe great thanks to NSERC, those affiliated with the Duluth REU who gave me Kathryn Hare, Frank Zorzitto, and especially Stan feedback on my P-orderings paper. Burris for my summer research terms, which have made all this possible. At the University of Water- Honorable Mention: Karen Yeats loo I also want to thank everyone in Math and Pure Citation Math for making it clear to me that I was in the right The Morgan Prize Committee is pleased to award place from the very beginning, and in Halifax to honorable mention for the 2003 Morgan Prize for everyone who encouraged me on the contests. Undergraduate Research to Karen Yeats for a series of outstanding contributions on topics ranging from asymptotics and number theory to mathe- matical logic. A few examples indicate the broad versatility of her research. One of Karen Yeats’s research projects is moti- vated by a precise analogy between results in addi- tive number theory and results in multiplicative number theory. Based on this analogy, Karen Yeats APRIL 2004 NOTICES OF THE AMS 439.
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