Mathematical Sciences: Topology of Complex Projective Curves and Surfaces

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9307896 Hironaka This awards supports the research of Professor E. Hironaka to work in algebraic geometry. Topics to be studied include the geometry of complex varieties, especially smooth surfaces and embedded curves. In particular she hopes to find ways to compute Betti numbers for these geometric objects. The research is in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which blossomed to the point where it has, in the past 10 years, solved problems that have stood for centuries. Originally, it treated figures defined in the plane by the simplest of equations, namely polynomials. Today, the field uses methods not only from algebra, but also from analysis and topology, and conversely it is extensively used in those fields. Moreover it has proved itself useful in fields as diverse as physics, theoretical computer science, cryptography, coding theory and robotics. ***