*January 2005, Atlanta, GA*

In 1990, the Executive Committee of the Association for Women in Mathematics (AWM) established the annual Alice T. Schafer Prize for excellence in mathematics by an undergraduate woman. The prize is named for former AWM president and one of its founding members, Alice T. Schafer (Professor Emerita from Wellesley College), who has contributed a great deal to women in mathematics throughout her career. The criteria for selection includes, but is not limited to, the quality of the nominees' performance in mathematics courses and special programs, an exhibition of real interest in mathematics, the ability to do independent work, and if applicable, performance in mathematical competitions.

AWM is pleased to present the Fifteenth Annual Alice T. Schafer Prize to **Melody Chan**, Yale University.

Additionally, AWM was pleased to recognize **Margaret I. Doig**, a senior major at University of Notre Dame, and **Elena Fuchs**, a senior mathematics major at University of California, Berkeley who were selected as runners-up in the Schafer Prize competition. AWM was further pleased to recognize **Annalies Vuong**, University of California, Santa Barbara as an honorable mention recipient in the Schafer Prize competition.

### Schafer Prize Winner: Melody Chan

Melody Chan is a senior at Yale University where she excelled in a wide variety of mathematics courses and was awarded the prestigious Hart Lyman Prize. She has made presentations at the Yale Math Club, earned an honorable mention on the Putnam Competition and is Vice President of the Yale chapter of Phi Beta Kappa. Melody also did outstanding work in advanced courses at the Budapest Semester in Mathematics in Hungary.

Melody participated in an REU at East Tennessee State University where she investigated the pebbling number problem. Her approach to the problem was described as “ingenious,” and she able to significantly improve on the bounds for the pebbling number of a graph with n vertices. She gave a well-received talk on this work at the Joint Mathematics Meetings in 2003, and her results have been submitted for publication.

In the summer of 2004, Melody participated in an REU at the University of Minnesota at Duluth during which she wrote three professional level papers on the concept of the distinguishing number. In the first paper, she was able to answer a long-standing open question, dating from the paper in which the distinguishing number was introduced. In her subsequent papers, she took a group-theoretic approach to the distinguishing number problem. This work exhibited a mastery of groups acting on sets. Various experts in the field described her papers as “remarkable” and “beautiful work” and a “foundational contribution” to the field that will likely be frequently cited.

**Response from Melody Chan**

I am truly happy to be able to accept the 2005 Alice T. Schafer Prize from the Association for Women in Mathematics. I view this prize as both an honor and a responsibility. The AWM fills an invaluable role in encouraging women to pursue mathematical careers, and I can only hope to contribute to the pursuit of its commendable goals.

So many people deserve my most profound thanks for their support. In particular, I would like to thank Richard Beals and Dana Angluin, two of my professors at Yale without whose guidance and excellent teaching I would be a very different person and mathematician. I would also like to thank Anant Godbole and Joseph Gallian for their wonderful REU programs at East Tennessee State University and at the University of Minnesota Duluth, Finally, I would like to thank my research advisors at Duluth, Melanie Wood and Philip Matchett, who have helped me so much at every stage of the mathematical research process.

### Schafer Prize Runner-Up: Margaret 1. Doig

Margaret 1. Doig is a senior honors mathematics major at the University of Notre Dame. Her impressive credentials include being the 2001 Notre Dame high scorer on the Putnam, a year spent at Oxford University being tutored by, among others, number theorist Susan Howson and topologist Wilson Sutherland, and receiving the Goldwater Scholarship.

Margaret’s research at the University of Minnesota at Duluth REU during the summer of 2003 resulted in the paper “Maximum Run Length in a Toriodal Grid Graph”. She presented this work at the 2004 Joint Mathematics Meetings in Arizona. Next, she spent the summer of 2004 doing research on braid groups with Frank Connolly. Specifically, they worked on the Right Angled Artin Conjecture of Abrams and Ghrist, which they believe they have solved. Margaret made a particularly substantial contribution by developing a crucial technique. This work will result in two papers, one by her alone that will detail the technique, and one coauthored with Connolly. For her senior thesis, supervised by Claudia Polini, Margaret further extends her areas of mathematical expertise to include commutative algebra and algebraic geometry.

**Response from Margaret 1. Doig**

I am very grateful to the Association for Women in Mathematics for this honor. The encouragement and care of the organization are tremendously important, and I hope to be able to make an equivalent return someday. I am thankful to Joe Gallian and the rest of the Duluth REU for teaching me what it means to do math, and I greatly appreciate the excellent education I have received from the Notre Dame community, especially from Frank Connolly. Not to be overlooked is the contribution of my high school mentors Wright Vermilya and Tom Brieske.

### Schafer Prize Runner-Up: Elena Fuchs

Elena Fuchs is a senior at the University of California at Berkeley. Her coursework, which includes a number of graduate courses, has been called “especially incisive” and “quite clever”. Her instructors comment on her advanced mathematical maturity.

During the summer of 2003 Elena attended the Penn State University MASS program. One outcome of her work was a paper coauthored with Paul Baginski on modular invariants of elliptic curves. Her work at the University of Minnesota at Duluth REU during the summer of 2004 resulted in a paper entitled “Longest Induced Cycles in Cayley Graphs,” which has been submitted for publication. For her senior thesis, she returns to the impressively complicated topic of elliptic curves. Under the direction of Ken Ribet, she will study endomorphisms of the Jacobian of hyperelliptic curves.

**Response from Elena Fuchs**

It is a great honor to be selected as runner-up to the Alice Schafer Prize. I would like to thank the Association for Women in Mathematics for the encouragement and recognition they offer young women pursuing math--this award is only one of the many ways in which it promotes emerging female mathematicians. I am also deeply grateful to Professor Ken Ribet, who has truly inspired me in my research and studies, for his invaluable teaching, as well as his patience and guidance. Thank you to Professor Gallian and everyone at his wonderful Duluth REU, which has been one of the most rewarding experiences in my mathematical career thus far. As always, I want to thank my family and friends for supporting me in all of my endeavors. A special thanks to my father, who has been more than just a mathematical role model to me for many years.

### Honorable Mention: Annalies Vuong

Annalies Vuong is a senior at the University of California at Santa Barbara. She is the founding president of the UCSB Mathematics Students’ Association and already a regular attendee of the graduate students seminars in topology and differential geometry. Annalies is proving to be a rising star, excelling in coursework and in the research setting.

In the Summer 2003 Annalies Vuong participated in the Carleton/St. Olaf College Program for Undergraduate Women in Mathematics. During the Summer 2004 at the East Tennessee State University REU program, Annalies came into her own. She worked on four different problems in combinatorics and graph theory, which led to three (perhaps four) papers submitted for publication. One recommender described her as fearless, focused, and unrelenting and furthermore knowing exactly when to stop a particular line of investigation and investigate other avenues. Annalies Vuong combines talent, energy, determination and a passion for mathematics.

**Response from Annalies Vuong**

I would like to thank the Association for Women in Mathematics for this honor. I am tremedously grateful for their support, as well as for the support of the mathematics department at UCSB and the College of Creative Studies. rye been very lucky to have so many people encourage my love of math and help me to succeed in mathematics; in particular, I’d like to thank Anant Godbole for his East Tennesee State University REU. I had an amazing experience doing math there, thanks to his boundless enthusiasm and belief in his students. I’m also endebted to Kasra Rafi, John Ennis, and Jeffrey Stopple for their encouragement and to everyone involved with the Carleton Summer Math Program for Women.