2007 Meeting Program

Sums of Squares and the 290-Theorem
Manjul Bhargava, Princeton University

Abstract: The famous "Four Squares Theorem" of Lagrange asserts that any positive integer can be expressed as the sum of four square numbers. That is, the quadratic form a^2 + b^2 + c^2 + d^2 "represents" all (positive) integers. When does a general quadratic form represent all integers? When does it represent all odd integers? When does it represent all primes? We show how all these questions turn out to have very simple and surprising answers. In particular, we describe the recent work (joint with Jonathan Hanke, Duke University) in proving Conway's 290-Conjecture.

Speaker Biography: Manjul Bhargava is a professor of mathematics at Princeton University and has research interests in algebraic number theory and representation theory. He graduated from Harvard University in 1996 and received his doctorate from Princeton in 2001. His highly acclaimed Ph.D. thesis, work conducted under Andrew Wiles, generalized the classical Gauss composition law for quadratic forms. Professor Bhargava has won numerous awards for his outstanding research including the SASTRA Ramanujan Prize, the Clay Research Award and the Frank and Brennie Morgan Prize. He was named one of Popular Science magazine's Brilliant 10 in 2002.

Preference Sets, Graphs, and Voting in Agreeable Societies
Francis Edward Su, Harvey Mudd College

Abstract: When mathematical objects have a social interpretation, the associated theorems have social applications. We give examples of situations where sets model preferences, and suggest extensions of classical theorems on convex sets which have applications to the analysis of voting in "agreeable" societies. This talk features research with undergraduates.

Speaker Biography: Francis Edward Su earned his Ph.D. from Harvard University, held visiting positions at Cornell and MSRI, and is now Professor of Mathematics at Harvey Mudd College. His research focuses on problems in topological and geometric combinatorics, especially those that have applications to the social sciences, and he has co-authored many papers with undergraduates. He has a passion for teaching and popularizing mathematics. In 2001 he received the Merten M. Hasse Prize from the MAA for expository writing, and in 2004 he received the MAA's Henry L. Alder Award for distinguished teaching. Su serves on the editorial boards of Math Horizons and the American Mathematical Monthly, and is author of the popular Math Fun Facts website that receives 3,000 hits per day. For fun he enjoys songwriting, swing dancing, sports, and theological reflection.

Panel: The Situation Today: Continuing Challenges for Girls and Women in Mathematics

Panelist Biography: Joan Birman is a native New Yorker. She attended Swarthmore College and Barnard College of Columbia University as an undergraduate.  She earned an M.S. in Physics from Columbia and worked for various companies that designed electronic equipment for aircraft before returning to school to pursue graduate studies at the Courant Institute of Mathematical Sciences at New York University.  She receive her Ph.D. from Courant with the dissertation "Braid Groups and Their Relationship to Mapping Class Groups".  After teaching for a few years at the Stevens Institute of Technology, Birman joined the faculty at Barnard College where she has been since 1973.  Dr. Birman has received numerous honors and awards during her career including a Sloan Foundation Fellowship, a Guggenheim Fellowship, the New York City Mayor's Award for Excellence in Science and Technology and the MAA's Chauvenet Prize for expository writing.  She is currently Research Professor Emeritus at Barnard.

Panelist Biography: Mary E. Morley is a mathematics senior content specialist at the College Board.  She previously served as a development scientist at the Assessment and Scoring Center of the Educational Testing Service, where she received the ETS Scientist Award.  Prior to her time at ETS, she was an assistant professor of mathematics at Temple University in Philadelphia, and was a post-doctoral fellow at Purdue University.  Dr. Morley earned her M.S. and Ph.D. degrees in Mathematics from the University of Chicago.

Panelist Biography: Olof Bjorg Steinthorsdottir is an assistant professor of mathematics education the University of North Carolina in Chapel Hill. She studies the teaching and learning of mathematics. Her research interests include students' understanding of mathematics, especially their understanding of whole numbers, fractions and proportion, and how gender, class, race and culture impact students' learning experiences and achievement.  She is currently further investigating the PISA 2003 results, where Iceland was the only country that showed gender difference in mathematics in favor of girls. She is also working on a research program in Iceland studying how pre-school students come to understand numbers and operations. Her goal is to impact both the pedagogical practices of pre-school teachers and to encourage the development of systematic mathematical work in pre-schools in Iceland. Prior to her graduate work she was a Middle School and High School teacher in her native Iceland.

Panelist Biography: Abbe Herzig (moderator) is an assistant professor of mathematics education at the University at Albany, State University of New York. Her research concerns equity and social justice in mathematics and science education at all levels. She is at the beginning of a 6-year research program concerning women and students of color in the post-graduate mathematical sciences, and is also investigating the low numbers of students of color in undergraduate engineering. She has developed courses and programs to help diverse populations of young people discover the relevance of mathematics and science to their interests and realities. She worked for 12 years as a statistician, much of that time for Consumers Union, the publisher of Consumer Reports magazine. She has consulted for the United Nations, the Yale School of Medicine, Brookhaven National Laboratory, and the Legal Defense Fund of the NAACP.

Contributed paper schedule and abstracts (Word)