杨晓奎 - 清华大学 - 数学科学系

个人简介

2012年毕业于美国加州大学洛杉矶分校(UCLA),主要从事几何分析、复几何与复代数几何领域的研究工作。他运用微分几何和代数几何，复分析，PDE等综合技术揭示了微分几何的中曲率和代数几何正性之间的深刻联系，完全解决了菲尔兹奖获得者丘成桐教授在上个世纪八十年代提出的若干著名猜想。在《Invent. Math》,《Camb. J. Math.》, 《 J. Differential Geom.》,《Amer. J. Math.》,《J. Math. Pures Appl.》，《Math. Ann.》,《J. Inst. Math. Jussieu》，《Compositio. Math.》，《J. Algebraic Geom.》，《Trans. AMS》等国际一流杂志上发表论文三十多篇。工作履历 2019-现在，清华大学数学系/丘成桐数学科学中心，教授 2016-2018，中国科学院数学所，研究员 2015-2016，中国科学院数学所，副研究员 2012-2015，美国西北大学，Boas助理教授奖励与荣誉 2018年华人数学家联盟最佳论文奖

研究领域

复几何、几何分析、复代数几何

近期论文

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(with B.-L. Chen) On Euler characteristic and fundamental groups of compact manifolds To appear in Math Ann. ___________, RC-positivity, vanishing theorems and rigidity of holomorphic maps J. Inst. Math. Jussieu. 20 (2021), no. 3,1023-1038. ___________, RC-positive metrics on rationally connected manifolds. Forum Math. Sigma 8(2020), Paper no 53. ___________, Scalar curvature, Kodaira dimension and A-genus. Math. Z. 295(2020), 365-380. (with D. Li, W.-H. Ou) On projective varieties with strictly nef tangent bundles. J. Math. Pures Appl. 128 (2019), 140-151. ___________, A partial converse to the Andreotti-Grauert theorem. Compositio Math. 155 (2019), 89-99. ___________, Scalar curvature on compact complex manifolds. Tran. Amer. Math. Soc. 371 (2019), 2073-2087. __________, RC positivity, rational connectedness and Yau's conjecture. Camb. J. Math. 6 (2018), 183-212. (with V. Tosatti, B. Weinkove), The K?hler-Ricci flow, Ricci-flat metrics and collapsing limits. Amer. J. Math. 140 (2018), 653-698. (with B.-L. Chen) Compact K?hler manifolds homotopic to negatively curved Riemannian manifolds. Math. Ann. 370 (2018), 1477-1489. (with F.-Y. Zheng), On real bisectional curvature for Hermitian manifolds. Tran. Amer. Math. Soc. 371 (2018), 2703-2718. (with V. Tosatti), An extension of a theorem of Wu-Yau. J. Differential Geom. 107 (2017), 573-579. __________, Big vector bundles and compact complex manifolds with semi-positive tangent bundle. Math. Ann. 267 (2017), 251-282. (with K.-F. Liu), Ricci curvatures on Hermitian manifolds. Tran. Amer. Math. Soc. 369 (2017), 5157-5196. ___________, Hermitian manifolds with semi-positive holomorphic sectional curvature. Math. Res. Lett. 23 (2016), 939-952. (with V. Tosatti, Y. Wang, B. Weinkove) C2,αestimates for nonlinear elliptic equations in complex and almost complex geometry. Calc. Var. PDE. 54 (2015), 431-453. (with V. Tosatti, B. Weinkove) Collapsing of the Chern-Ricci flow on elliptic surfaces. Math. Ann. 362 (2015), 1223-1271. (with K.-F. Liu, S. Rao) Quasi-isometry and deformations of Calabi-Yau manifolds. Invent. Math. 199 (2015), 423-453. (with K.-F. Liu) Curvatures of direct image sheaves of vector bundles and applications I. J. Differential Geom. 98 (2014), 117-145. (with K.-F. Liu, X.-F. Sun) Positivity and vanishing theorems for ample vector bundles. J. Algebraic Geom. 22 (2013), 303-331.