*January 2007, New Orleans, LA*

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 Seventeenth Annual Alice T. Schafer Prize to **Ana Caraiani,** Princeton University.

Additionally, AWM was pleased to recognize **Tamara Broderick**, Princeton University, and **Yaim Cooper**, MIT, who were selected as runners-up in the Schafer Prize competition. AWM was further pleased to recognize **Alyson Deines**, Kansas State University as an honorable mention recipient in the Schafer Prize competition.

### Schafer Prize Winner: Ana Caraiani

**Ana Caraiani** is a senior at Princeton University, and she is already conducting professional-level mathematical research. In the summers of 2005 and 2006, Caraiani participated in the REU program at the University of Minnesota at Duluth. She worked independently on a project on semigroups of rational numbers, related to the 3x + 1 problem. Her work on this problem is highly praised. The resulting paper, “On Wild Semigroups,” introduces new ideas that exhibit significant ingenuity.

Caraiani’s coursework at Princeton has been remarkable. She has done very well in extremely difficult classes, and is noted for her independence and mathematical sophistication. One professor has said that her work “made you think that it was a professional mathematician who was answering the problems.” Another professor rates her among the top undergraduate mathematics majors in fifty years at Princeton.

Caraiani has won the William Lowell Putnam competition twice, scoring among the top five competitors in both her freshman and sophomore years, and is the only woman ever to have done so. The Princeton math department awarded her the Class of 1861 Prize her sophomore year and the Andrew H. Brown prize for outstanding juniors. She is expected to become a major mathematical figure and a world class research mathematician.

**Response from Ana Caraiani**

I am extremely honored to receive the Alice T. Schafer Prize and to be recognized along with so many distinguished women in mathematics. I would like to thank the Association for Women in Mathematics for inspiring women to excel in math. This award has certainly encouraged me to aim higher and to set new standards for my work in the hope that I would live up to the expectations associated with such an honor.

I would not have made it this far without the support of many people over the last several years. I would first like to thank my math teacher, Liana Manu, for nurturing my interest in math before and throughout high school. I am also very grateful to Joe Gallian for inviting me to his REU in Duluth, finding the best suited problem for me, and for believing in my abilities even more than I did. The Princeton math department has provided the best environment I could have asked for in which to learn math. I am especially grateful to Robert Gunning for introducing me to an amazing new field and letting me share in his enthusiasm for its elegance. I would like to extend my deepest thanks to Andrew Wiles for entrusting me with a senior thesis problem and for all of his support and guidance in approaching it. I am also indebted to John Conway for suggesting an exciting problem for my junior paper and to William Browder for a challenging yet rewarding reading course. There are many other professors at Princeton whose excellent teaching and encouragement have been indispensable and I thank them all.

### Schafer Prize Runner-Up: Tamara Broderick

**Tamara Broderick** is a senior at Princeton University. A Goldwater scholar, Broderick was awarded the George B. Wood Legacy Sophomore Prize for her exceptional achievements during her sophomore year, and the Princeton Class of 1939 Prize at the end of her junior year for achieving the highest standing in all preceding college work at Princeton. She is described by her professors as “one of the very, very best,” “extraordinarily talented and intelligent,” “bursting with drive, energy and an unquenchable thirst for knowledge.”

For her junior paper at Princeton, Broderick developed a mathematical model of animal movement based on radio telemetry data, and she is currently engaged in research on drifting games.

In the summers of her sophomore and junior years, Broderick participated in the Director’s Summer Program at the National Security Agency and worked on problems involving cryptoanalysis, data mining, combinatorics, statistics and numerical analysis. She quickly emerged as a team leader in each problem she attacked, and as a result she published two internal classified papers each summer at NSA. Being the outstanding problem solver amongst all participants, Broderick was selected, after her first summer at NSA, to represent the United States during the following summer at a student exchange program with the GCHQ, an intelligence and security organization in the United Kingdom. A correspondent from GCHQ comments that Broderick’s work “will no doubt shape further work by GCHQ analysts”.

In addition to being an outstanding mathematician, Broderick serves as a leader in numerous math-related activities at Princeton; amongst others she is the current president of the Math Club. Broderick’s professors predict she will have an extraordinary career arc in mathematics.

**Response from Tamara Broderick**

I am honored and excited to be selected as a Runner-Up for the Alice T. Schafer Prize. My thanks go first and foremost to the AWM not only for their recognition but also for their wonderful encouragement of women in mathematics by means of concrete and far-reaching initiatives.

I was lucky enough to have female mathematicians showing me the ropes from the very beginning. My gratitude goes out to my middle school math teacher Ms. Vega for seeing early potential, to Ellen Stenson for coming to my high school and giving us a multivariable calculus class, to Ingrid Daubechies for agreeing to be our Princeton Math Club faculty adviser, and to countless other female mentors and role models. I would also like to thank Reza Beigi and Jeanne Stephens for their unfailing encouragement of my pusuit of mathematics though their fields are, respectively, physics and English, Elias Stein for his amazing and beloved analysis series at Princeton, and all of the good mathematics teachers from whom I have had the pleasure of learning. Finally, I am deeply grateful to Robert Schapire for his clear and thoughtful classroom instruction, endless research guidance, and boundless support for this aspiring mathematician.

I’ve always had the sense that there was something both magical and powerful to mathematics, and I am lucky to have so many people and opportunities to regularly refresh my sense of wonder at the field.

### Schafer Prize Runner-Up: Yaim Cooper

**Yaim Cooper** is a senior at the Massachusetts Institute of Technology. Her outstanding success in a vast array of both undergraduate and graduate mathematics courses has been augmented by her research at the Louisiana State University and the University of Wisconsin REUs. Cooper’s “exceptional vigor and zeal” for mathematics becomes apparent with her achievements.

At the LSU REU, Cooper investigated the Ihara zeta function of a graph. Impressively, under a non-partiteness condition, she gave an elementary proof of a theorem due to Bass and generalized an important example appearing in a doctoral dissertation. She has submitted her results for publication in a major combinatorics journal. Showing her breadth, Cooper's research at the Wisconsin REU focussed on the completely different mathematical area of modular forms. Her REU team was asked to generalize a theorem of Serre on congruence properties of the classical j-function. Led by Cooper they “nicely obtained what is surely the best generalization.” Their significant joint paper is expected to appear in an international number theory journal. Cooper is also active in the undergraduate math club and has started two new lecture series at MIT.

**Response from Yaim Cooper**

I am honored to have been selected as a runner-up for the Alice T. Schafer prize. However much of the recognition should be directed at the people who have helped me along the way. First, I thank my parents, for giving me so many opportunities. I’d like to also thank Professor Lee Stout, who helped me far beyond what was required of him, and helped me learn and love math during my critical high school years. I was lucky to spend two wonderful summers doing math research, and am grateful to Professors Robert Perlis and Ken Ono for giving me a delightful introduction to math research, and the interesting topics they guided me to. I also must thank my peers at both REUs, in particular my coauthors from last summer, Nick Wage and Irena Wang. At MIT, Professor Pavel Etingof has been a wonderful advisor, and I thank Professor Steven Kleiman for introducing me to commutative algebra and algebraic geometry, in such a way that has made me want to learn a lot more of it!

### Schafer Prize Honorable Mention: Alyson Deines

**Alyson Deines** is a senior math major at Kansas State University. Her mathematical maturity, talent, energy, and initiative have been demonstrated by the many activities and research projects in which she has participated and excelled.

In 2005, Deines participated in the Budapest Semesters in Math program and in the REU program at the University of Nebraska. Her team of three students at the Nebraska REU worked on a mathematical biology problem involving the population dynamics of peregrine falcons. This work has been submitted to a journal on ecology and has been presented at several meetings. In 2006, Deines took part in the Director’s Summer Program at the National Security Agency. In this program, she was the leader of a group of students working on a problem of statistical regression of real-time streaming data. Her team developed an extremely robust model in the stream environment, making a major improvement in this important problem. Their work has been published internally at NSA.

Deines is currently a Goldwater scholar and she is also the recipient of a Clare Boothe Luce Scholarship from the Women in Engineering and Science program at Kansas State. She has excelled in a rigorous program of both undergraduate and graduate level courses. She is the president of the Kansas State Math Club and has demonstrated great enthusiasm and energy for mathematics as well as focus and drive. In the words of one recommender, she is “well started on a promising mathematics career.”

**Response from Alyson Deines**

I am thrilled to be recognized as honorable mention for this year’s Alice T. Schafer prize. I would like to thank the Association for Women in Mathematics for all the encouragement they give females in mathematics. The encouragement and advice of female mathematicians has been crucial to discovering my passion for mathematics. I am grateful that this association provides such strong support and creates positive experiences for other women in the field. Specifically, I would like to thank my advisor, Marianne Korten, of Kansas State University. She gives solid advice and encouragement to me and other females in the Kansas State University Math Department. I would also like to thank Richard Rebarber, from the University of Nebraska-Lincoln, and Joe McCloskey, who have enthusiastically guided me through my summer research projects. Furthermore, I would like to thank Todd Cochrane, of Kansas State University, my current research advisor, for introducing me to number theory and guiding me through research in this area. Many other professors at Kansas State University have also given me invaluable support. Finally, I must thank my parents for the encouragement they have and will always give me to pursue my interests.