9706707 Grassi This project is concerned with Calabi-Yau manifolds and their relation to physics. On the physics side, there are seven types of string theories, which are all consistent. Five of these theories are classical and two are new. The principal investigator will approach Calabi-Yau manifolds from different perspectives and analyze them by "patches". In particular, she will focus on dualities involving the two new string theories. This is research in the field of algebraic geometry. Algebraic geometry is 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.
