is a Japanese mathematician at Kyoto University specializing in algebraic geometry.
He introduced the FourierâÂÂMukai transform in 1981 in a paper on abelian varieties, which also made up his doctoral thesis. His research since has included work on vector bundles on K3 surfaces, three-dimensional Fano varieties, moduli theory, and non-commutative BrillâÂÂNoether theory. He also found a new counterexample to Hilbert's 14th problem (the first counterexample was found by Nagata in 1959).