This award supports the research in p-adic analysis and algebraic geometry of Professor Diane Meuser of Boston University. Dr. Meuser's project involves an investigation of the properties of p-adic complex powers, otherwise known as the Igusa local zeta function. In particular, she intends to explore the connections between the behavior of the local zeta function and the geometry of the algebraic variety from which this function is derived. This is research in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in physics, theoretical computer science, and robotics.
