This award supports the mathematical research of Professor Chih-Han Sah of the State University of New York at Stony Brook. Dr. Sah intends to continue his investigations in topics con- nected with the classical problem on scissors congruences as well as various related mathematical questions that have arisen in such disparate fields as mathematical physics, number theory, and functional analysis. This very interdisciplinary project connects physics with several of the most active areas of modern mathematics: algebra, topology, functional analysis. In one of the bridges that Dr. Sah has constructed between mathematics and physics, he found that a space curve related to the 4-state self-dual chiral Potts model in physics was precisely the degree-4 Fermat curve, of genus 3, long known to mathematicians and extensively studied by algebraic geometers. In another, related development, Dr. Sah has been active in explaining the "polylogarithms", mysterious functions arising as integrals of logarithms, which have been appearing both in physical and algebro-geometric research.
