Shigeru Mukai (向井 茂, Mukai Shigeru, born 1953) is a Japanese mathematician at Kyoto University specializing in algebraic geometry.

He introduced the Fourier–Mukai 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 Brill–Noether theory.

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

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