# In 1990, the Executive Committee of the Association for Women in Mathematics (AWM) established the 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 emeritus from Wellesley College), who has contributed a great deal to women in mathematics throughout her career. The criteria for selection include, but are 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 twentieth annual Alice T. Schafer Prize to the co-winners **Hannah Alpert**, University of Chicago, and **Charmaine Sia**, Massachusetts Institute of Technology

Additionally, the accomplishments of three outstanding young women, all senior mathematics majors, were recognized on Wednesday, January 13, 2010. AWM was pleased to honor **Anna Lieb**, University of Colorado, Boulder, as runner-up for the 2010 Schafer prize competition. **Megan Bernstein**, University of California, Berkeley, **Ruthi Hortsch**, University of Michigan, and **Laura Starkston**, Harvard University were recognized as honorable mention recipients in the Schafer prize competition. Their citations are available from the AWM.

### Schafer Prize Co-Winner: Hannah Alpert

**Hannah Alpert**, a junior at the University of Chicago and a Goldwater scholar, approaches mathematics "with great conceptual understanding and a fierce tenacity." Her performance in her classes has been superb. She began her research career even before she started college, co-authoring a paper on topological graph theory. After her first year in college, Alpert attended the Willamette Valley Research Experience for Undergraduates, where her rapid resolution of suggested problems drove her supervisor to present more. Her (co-authored) paper on obstacle numbers of graphs has been accepted; the corresponding poster presentation was awarded an MAA Undergraduate Poster Session prize in 2009.

Alpert spent summer 2009 at the Duluth REU. Remarkably, she has written and submitted for publication three sole-authored papers in three different areas based on her work there. In one, she determined the $k$-ranking numbers of 3 by $n$ grid graphs, using "innovative" methods that also "give tremendous insight into the general case." She has been invited to present the results of another, on finite phase transitions in countable abelian groups, in a graduate seminar.

Alpert's mentors paint a consistent picture of a remarkably mature young mathematician, one who is a creative problem solver with a "formidable talent." Over and over, she has solved challenging open problems in elegant and fully original ways. One letter writer compares her to a Nobel Prize winner he taught; others describe her as "incredible," "fantastic," and "destined to become a first-rate mathematician."

**Response from Hannah Alpert**

I would like to thank the AWM for selecting me this year as a co-winner of the Schafer Prize. The award represents the efforts of many advisers who have advocated for me and insisted that all the best opportunities be open to me. Most of all I am grateful to Sarah-Marie Belcastro, for many years of work aggressively supporting my mathematical education. Joe Gallian, Josh Laison, and Paul Sally have also worked hard on my behalf. I am glad their efforts are being recognized in this prize, and I am confident that they will continue to render mathematics careers more and more accessible to young women.

### Schafer Prize Co-Winner: Charmaine Sia

**Charmaine Sia** is a senior at Massachusetts Institute of Technology, where she has excelled in both undergraduate and graduate classes. She has a perfect undergraduate transcript. To quote one of her recommenders, “Charmaine absorbs mathematics like a sponge.” Another one writes, “I have never seen a student with as voracious an appetite for knowledge.”

In addition to her academic performance, Sia is also an expert contest-taker with three bronze medals at the International Mathematical Olympiad and a top 75 ranking in the Putnam Mathematical Competition. In her three years as an undergraduate, Sia has already gained extensive research experience. She has written four papers, two of which are single-authored. Sia has spent the past three summers in undergraduate research programs, starting with SPUR at MIT in 2007, where she won the prize for best research in the program for her work on zero-sum problems in finite group theory. The next summer she participated in the Duluth REU program, where she wrote two papers, one on classifying the orbits of special groups under the Hurwitz action, and the other on game chromatic numbers of products of graphs. Both papers have been published in professional journals. In the summer of 2009, Sia participated in the SMALL research program at Williams College, where she co-authored two papers on knot theory. She was in charge of one of these papers. Her mentor there writes, “Charmaine single-handedly made rigorous the very difficult collection of ideas that we discussed, but as a group understood incompletely. […] she did a better job […] than I could have done myself.”

Sia is, in the words of her teachers and mentors, an “astonishing” student who “has distinguished herself in every possible way” and “already a mature mathematician” with “immense potential.” She is expected to become an outstanding research mathematician.

**Response from Charmaine Sia**

I am very honored to be a co-winner of the Alice T. Schafer Prize. I would like to thank the AWM for their invaluable role in encouraging and supporting women in mathematics. I am grateful to several people who have guided, encouraged, and supported me thus far. I would first like to thank my family, who has constantly supported my pursuit of mathematics. I thank my instructors in the Singapore IMO program for nurturing my interest in mathematics. I also thank Hoda Bidkhori, who provided much guidance and encouragement on my first research paper at SPUR. I am especially grateful to Joe Gallian and Colin Adams for their wonderful REU programs in Duluth and Williams College respectively, which gave me the opportunity to interact with other extremely talented mathematics students there. Finally, I would like to thank the many people, in particular the MIT mathematics department, who generously shared their wisdom and knowledge with me, and from whom I benefited immensely.