is a Japanese

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

Kyoto University , or , is a National university, national research university in Kyoto, Japan. Founded in 1897, it is one of the former Imperial Universities and the second oldest university in Japan. The university has ten undergraduate faculties, eighteen gra ...

specializing in

algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

Work

He introduced the

Fourier–Mukai transform In algebraic geometry, a Fourier–Mukai transform ''Φ'K'' is a functor between derived categories of coherent sheaves D(''X'') → D(''Y'') for schemes ''X'' and ''Y'', which is, in a sense, an integral transform along a kernel object ''K'' � ...

in 1981 in a paper on

abelian varieties In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a smooth projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular f ...

, which also made up his doctoral thesis. His research since has included work on

vector bundle In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to eve ...

s on

K3 surface In mathematics, a complex analytic K3 surface is a compact connected complex manifold of dimension 2 with а trivial canonical bundle and irregularity of a surface, irregularity zero. An (algebraic) K3 surface over any field (mathematics), field ...

s, three-dimensional

Fano varieties In algebraic geometry, a Fano variety, introduced by Gino Fano , is an algebraic variety that generalizes certain aspects of complete intersections of algebraic hypersurfaces whose sum of degrees is at most the total dimension of the ambient proje ...

moduli theory In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects. Such spac ...

, and non-commutative

Brill–Noether theory In algebraic geometry, Brill–Noether theory, introduced by , is the study of special divisors, certain divisors on a curve that determine more compatible functions than would be predicted. In classical language, special divisors move on the cu ...

. He also found a new counterexample to Hilbert's 14th problem (the first counterexample was found by Nagata in 1959).

Publications

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References

External links

* * 1953 births 20th-century Japanese mathematicians 21st-century Japanese mathematicians Algebraic geometers Kyoto University alumni Academic staff of Kyoto University Living people Academic staff of Nagoya University {{Japan-mathematician-stub