With his collaborator Ngaiming Mok, he has developed the theory of varieties of minimal rational tangents, which combines methods of algebraic geometry and differential geometry in the study of rational curves on algebraic varieties. He has applied this theory to settle a number of problems on algebraic varieties covered by rational curves.[1]
In 2020, he was the founding director of the Center for Complex Geometry at the Institute for Basic Science.[7] In 2023, he was selected to be on the committee for the Abel Prize.[8][9]
"Uniruled projective manifolds with irreducible reductive G-structures". Journal für die reine und angewandte Mathematik (Crelle's Journal). 1997 (491). Walter de Gruyter GmbH: 55–64. 1 September 1997. doi:10.1515/crll.1997.490.55. hdl:10722/75184. ISSN0075-4102. S2CID118051384.
Hwang, Jun-Muk; Mok, Ngaiming (2003). "Finite morphisms onto Fano manifolds of Picard number 1 which have rational curves with trivial normal bundles". Journal of Algebraic Geometry. 12 (4). American Mathematical Society (AMS): 627–651. doi:10.1090/s1056-3911-03-00319-9. hdl:10722/42125. ISSN1056-3911. S2CID56059732.
Hwang, Jun-Muk; Mok, Ngaiming (25 February 2005). "Prolongations of infinitesimal linear automorphisms of projective varieties and rigidity of rational homogeneous spaces of Picard number 1 under Kähler deformation". Inventiones Mathematicae. 160 (3). Springer Science and Business Media LLC: 591–645. Bibcode:2005InMat.160..591H. doi:10.1007/s00222-004-0417-9. hdl:10722/48613. ISSN0020-9910. S2CID52237844.
Fu, Baohua; Hwang, Jun-Muk (8 December 2011). "Classification of non-degenerate projective varieties with non-zero prolongation and application to target rigidity". Inventiones Mathematicae. 189 (2). Springer Science and Business Media LLC: 457–513. arXiv:1011.4751. doi:10.1007/s00222-011-0369-9. ISSN0020-9910. S2CID253736967.