MATHEMATICAL SCIENCES: ELLIPTIC THREEFOLDS AND CALABI-YAU THREEFOLDS

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9400873 Gross Professor Gross will study elliptic threefolds and Calabi-Yau threefolds. In particular he will study deformation classes of Calabi-Yau threefolds with a view to obtaining classification theorems. He also intends to further study the recently discovered phenomenon of mirror symmetry. This is research in the field of algebraic geometry, yet it directly connects to two of the great advances in theoretical physics in this century--quantum mechanics and general relativity. Algebraic geometry itself 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.