杨晓奎-清华大学数学科学中心

研究领域

复几何、几何分析、复代数几何。

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.》,《Compositio. Math.》，《J. Algebraic Geom.》，《J. Math. Pures Appl.》，《Math. Ann.》,《J. Inst. Math. Jussieu》，《Trans. AMS》,《Calc. Var. PDE.》等国际一流杂志上发表论文四十多篇。代表性论文有

1. ______, RC-positivity, vanishing theorems and rigidity of holomorphic maps. J. Inst. Math. Jussieu. 20 (2021), no. 3,1023-1038.

2. ______, A partial converse to the Andreotti-Grauert theorem. Compositio. Math. (2019), 89-99.

3. ______, RC-positivity, rational connectedness and Yau's conjecture. Camb. J. Math. (2018), 183-212.

4. Valentino Tosatti; ______, An extension of a theorem of Wu-Yau. J. Differential Geom. (2017), 573-579.

5. Kefeng Liu; Sheng Rao; ______, Quasi-isometry and deformations of Calabi-Yau manifolds. Invent. Math. (2015), 423-453.

6. Kefeng Liu; ______, Curvatures of direct image sheaves of vector bundles and applications. J. Differential Geom. (2014), 117-145.

教育背景

2012年加州大学洛杉矶分校（UCLA）博士

工作经历

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

荣誉与奖励

国家杰出青年科学基金(2023)

华人数学家联盟最佳论文奖(2018)

海外高层次引进人才青年项目(2015)

发表论文

1. (With L.-D. Zhang) New characterizations for spherical space forms and complex projective spaces.

To appear in Trans. AMS

2. ___________, RC-positivity and the generalized energy density I: rigidity.

To appear in J. Differential Geom.

3.(with W.-H. Ou, J. Liu) Projective manifolds whose tangent bundle contains a strictly nef subsheaf.

J. Algebraic Geom. 33(2024), 1-53.

4. (with B.-L. Chen) On Euler characteristic and fundamental groups of compact manifolds

Math Ann. 381(2021), 1723-1743.

5. ___________, RC-positivity, vanishing theorems and rigidity of holomorphic maps

J. Inst. Math. Jussieu. 20 (2021), no. 3,1023-1038.

6. ___________, RC-positive metrics on rationally connected manifolds.

Forum Math. Sigma 8(2020), Paper no 53.

7. (with D. Li, W.-H. Ou) On projective varieties with strictly nef tangent bundles.

J. Math. Pures Appl. 128 (2019), 140-151.

8. ___________, A partial converse to the Andreotti-Grauert theorem.

Compositio Math. 155 (2019), 89-99.

9. ___________, Scalar curvature on compact complex manifolds.

Tran. Amer. Math. Soc. 371 (2019), 2073-2087.

10.___________, RC positivity, rational connectedness and Yau's conjecture.

Camb. J. Math. 6 (2018), 183-212.

11. (with V. Tosatti, B. Weinkove), The Kähler-Ricci flow, Ricci-flat metrics and collapsing limits.

Amer. J. Math. 140 (2018), 653-698.

12. (with B.-L. Chen) Compact Kähler manifolds homotopic to negatively curved Riemannian manifolds.

Math. Ann. 370 (2018), 1477-1489.

13. (with V. Tosatti), An extension of a theorem of Wu-Yau.

J. Differential Geom. 107 (2017), 573-579.

14.__________, Big vector bundles and compact complex manifolds with semi-positive tangent bundle.

Math. Ann. 267 (2017), 251-282.

15. (with K.-F. Liu), Ricci curvatures on Hermitian manifolds.

Tran. Amer. Math. Soc. 369 (2017), 5157-5196.

16. (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.

17. (with V. Tosatti, B. Weinkove) Collapsing of the Chern-Ricci flow on elliptic surfaces.

Math. Ann. 362 (2015), 1223-1271.

18. (with K.-F. Liu, S. Rao) Quasi-isometry and deformations of Calabi-Yau manifolds.

Invent. Math. 199 (2015), 423-453.

19. (with K.-F. Liu) Curvatures of direct image sheaves of vector bundles and applications I.

J. Differential Geom. 98 (2014), 117-145.

20. (with K.-F. Liu, X.-F. Sun) Positivity and vanishing theorems for ample vector bundles.

J. Algebraic Geom. 22 (2013), 303-331.

所授课程