Siu, Yum-Tong2017-04-172002Siu, Yum-Tong. 2002. Some Recent Transcendental Techniques in Algebraic and Complex Geometry. In Proceedings of the International Congress of Mathematicians, Beijing, China, August 20-28, 2002, Volume I: 439-448.7-04-008690-5http://nrs.harvard.edu/urn-3:HUL.InstRepos:32192700This article discusses the recent transcendental techniques used in the proofs of the following three conjectures. (1) The plurigenera of a compact projective algebraic manifold are invariant under holomorphic deformation. (2) There exists no smooth Leviflat hypersurface in the complex projective plan. (3) A generic hypersurface of sufficiently high degree in the complex projective space is hyperbolic in the sense that there is no nonconstant holomorphic map from the complex Euclidean line to it.en-USPlurigeneraLevi-FlatHyperbolicityConference Paper2017-03-2620022017-04-17