Sep 13, 2010 - Claremont, Calif. - Francis Su, professor of mathematics, was awarded a National Science Foundation (NSF) grant that continues the line of work begun in his prior NSF grant in which methods from combinatorics, topology and geometry are used to study problems in mathematical economics and the social sciences; in particular, problems related to voting and fair allocation.

The three-year grant of $205,668, is for his Research in Undergraduate Institutions (RUI) proposal in the Division of Mathematical Sciences, titled  ”Triangulations, Set Intersections, Fair Division, and Voting.”

Su's prior work introduced methods from combinatorial topology and discrete geometry to the study of fair division questions and voting problems. The current project will support the the development of the mathematics behinds these tools and the solution of several combinatorial questions that have been motivated by his prior work, including: (1) the study of triangulations of cubes and simplotopes, (2) the further development of combinatorial fixed point theorems and constructive solutions, and (3) the development of set intersection theorems and associated applications in social choice theory and fair division. This project will also support the active participation of undergraduates in this research.

Informally speaking, a "fair division" problem asks: how can we divide a set of goods among parties in such a way that each can be satisfied according to some notion of fairness. Social choice theory asks: how does a society make a group choice (e.g., in an election) in a way that best aggregates the preferences of all the individuals?  Questions of fairness and social choice are of interest to political scientists, economists, and game theorists, and motivate interesting mathematical questions. The space of preferences and the preference sets of each person are often naturally geometric sets (e.g., convex, connected, polyhedral), and the desired solution is often at the intersection of such sets. This project
aims to prove mathematical theorems (e.g., about set intersections and triangulations of polyhedra) that have direct bearing on important problems in the social sciences involving voting and fairness.

Su's work has been recognized by the Mathematical Association of America with the Henry L. Alder Award for Distinguished Teaching by a Beginning College or University Mathematics Faculty Member (2004) and the Merten M. Hasse Prize for outstanding mathematical exposition (2001). In addition to his teaching and research activities, Su is the creator of the popular award-winning Math Fun Facts website. He is currently serving as first vice-president of the Mathematical Association of America.