For developing the theory of Varieties of Minimal Rational Tangents in algebraic geometry to solve several long-standing problems and proving Ax-Schanuel’s conjecture for Shimura varieties.

Ngaiming MOK

For developing the theory of Varieties of Minimal Rational Tangents in algebraic geometry to solve several long-standing problems and proving Ax-Schanuel’s conjecture for Shimura varieties.

Complex differential geometry, a core field of modern mathematics, plays an important role in theoretical physics and many branches of mathematics. Ngaiming Mok made two fundamental contributions in this field and in other related fields. The first contribution is the theory of varieties of minimal rational tangents (VMRT) in algebraic geometry that he developed with Jun-Muk Hwang. The basic notion of VMRT was derived from Mok’s earlier work in differential geometry and has been used to prove the Kähler rigidity of irreducible compact Hermitian symmetric spaces, as well as a conjecture of Lazarsfeld’s, concerning holomorphic maps from rational homogeneous spaces onto projective manifolds.

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The second contribution is his proof of Ax-Schanuel’s conjecture for Shimura varieties jointly with Jonathan Pila and Jacob Tsimerman. The original Schanuel's conjecture is a major conjecture in number theory. The Ax-Schanuel Theorem on any Shimura variety is an important analogue of Schanuel’s conjecture in hyperbolic geometry. The theorem of Mok et al. has become an important tool in arithmetic geometry.

Ngaiming Mok was born in Hong Kong, China in 1956 and received his Ph.D. from Stanford University in 1980. He is currently the Edmund and Peggy Tse Professor in Mathematics at the University of Hong Kong.