Name: Yujiro Kawamata Research Field: Algebraic Geometry (Birational Geometry of Higher Dimensional Algebraic Varieties) Key Words: algebraic variety, Kodaira dimension, vanishing theorem, base point free theorem, minimal model program, log terminal singularity, derived category Current research Invesigating the birational geometry of higher dimensional algebraic varieties by making the best use of the combinations of algebraic, geometric and analytic methods. The topics include the Kodaira dimension of algebraic fiber spaces, applications of the Hodge theory, a birational characterization of abelian varieties, classification of logarithmic algebraic varieties, singularities of pairs, extensions of vanishing theorems, minimal model program, base point free theorem, logarithmic deformation theory, applications of multiplier ideal sheaves, derived category of coherent sheaves on algebraic varieties. Prerequisites It takes long time to understand basic concepts in algebraic geometry because this field of mathematics has many interactions with other fields. But thanks to this fact, algebraic geometry is useful and has diverse applications. The language of algebraic geometry is abstract and it is difficult to grasp the meaning of technical terms at first. It is better to start reading books with concrete examples. For example, a textbook by Kirwan on algebraic curves is a nice book showing how mathematics learned up to the second year at the university is applied to algebraic geometry. A text book by Reid is also easily accesible. Shafarevich's textbook is longer but very good. One can proceed to the scheme theory after getting acquainted to the algebraic varieties. Hartshorne's is the standard textbook in scheme theory..