Minimal Model Program

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The principal investigator will conduct research on the birational classification of algebraic varieties, in which spectacular breakthroughs have been made recently. The principal investigator proposes to prove the remaining major conjectures of the minimal model program,namely the existence of minimal models, the abundance conjecture, termination of flips, and the conjecture of Alexeev-Borisov concerning boundedness of Fano varieties.Algebraic Geometry is one of the oldest and most challenging of areas of research in mathematics, which combines some very classicial geometry, for example that of conic sections and the more modern techniques of algebra, which have had some recent spectacular successes, for example the work of Wiles on Fermat's Last Theorem. The principal investigator is preparing a chapter of a book on some recent exciting work in higher dimensional geometry, whose aim is to disseminate the seminal work of Shokurov in a form which will be accessible to a wide audience. The investigator will also try to impart some of the interesting research in algebraic geometry to undergraduate and graduate students in his teaching.