This Presidential Young Investigator Award will enhance support for Randall L. Dougherty's research in several areas of set theory and computing: the structure of Borel equivalence relations; elementary embeddings from the set of sets below a given rank to itself; Fourier coefficients of measures on the Cantor set; Borel versions of standard algebraic results; graph algorithms for the Human Genome Program. These topics range from fundamental questions about the set theoretic foundations of mathematics to highly practical applications to algorithms concerned with DNA. The common thread is sophisticated combinatorics, whether infinite or finite.
