Mathematical Sciences: Global Differential Geometry and Singularities

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9628522 Adams This grant supports a group of six mathematicians at the University of Georgia with interrelated interests. Research areas lie in geometry and topology including Seiberg-Witten theory, characteristic classes of singular varieties, integrable systems and Hamiltonian dynamics, and the Schottky problem. Partial support is provided for travel, a workshop, two postdoctoral researchers, and several graduate students. Seiberg-Witten theory lies in the interface of geometric analysis, topology and algebraic geometry; it is a recent discovery motivated by problems in theoretical physics. In this theory, electric-magnetic duality plays a crucial role which states roughly that electricity and magnetism are two phases of a single underlying phenomenon.