Welcome to visit Junyan CAO's HomePage

• Email:  junyan.cao@unice.fr ;    If you can not reach me by the unice email (it happens sometimes !!!), please use the imj-prg email, which is still available :  junyan.cao@imj-prg.fr  

• Address:  Laboratoire de Mathématiques J.A. Dieudonné UMR 7351 CNRS, Université Côte d'Azur Parc Valrose 06108, NICE CEDEX 2, France

• Office: 623

• 2020.9- , Professeur, Université Côte D'Azur, Laboratoire J.A. Dieudonné 

• 2014.9 - 2020.8 ,  Maître de conférence, Sorbonne Université (old name: Université Pierre et Marie Curie, Paris 6), Institut de Mathématiques de Jussieu

• 2013.11- 2014. 8,  Research Fellow, Korea Institute for Advanced Study (KIAS),  Mentor: Mihai Păun

• 2010-2013 Ph.D., Mathematics, Université de Grenoble I, Advisor: Jean-Pierre Demailly

• 2007-2010 M.S., Ecole Polytechnique

• 2003-2007 B.S., Mathematics, Fudan University 

ANR Karmapolis  with Benoît Cadorel, Ya Deng and Henri Guenancia. 

Publications

1. Geometry of K-trivial Moishezon manifolds : decomposition theorem and holomorphic geometric structures (with Indranil Biswas,  Sorin Dumitrescu, Henri Guenancia)

2. ddbar lemmas and a conjecture of O. Fujino (with Mihai Păun)

3. Hermite-Einstein metrics in singular settings (with Patrick Graf, Philipp Naumann, Mihai Păun, Thomas Peternell, Xiaojun Wu)

4. Direct images of pseudoeffective cotangent bundles (with Andreas Höring)

5. Frobenius integrability of certain p-forms on singular spaces  (with Andreas Höring), to appear in Comptes Rendus Mathématique, special volume in memory of Jean-Pierre Demailly

6. Infinitesimal extension of pluricanonical forms (with Mihai Păun)

7. Curvature formula for direct images of twisted relative canonical bundles endowed with a singular metric (with H. Guenancia and M. Păun)  Ann. Fac. Sci. Toulouse Math. (6) 31 (2022), n°3, special volume in honor of Ahmed Zeriahi

8. On the Ohsawa-Takegoshi extension theorem (with M. Păun, Bo Berndtsson), to appear in Journal of Geometric Analysis

9. Projective klt pairs with nef anti-canonical divisor (with F. Campana and S.-I. Matsumura) Algebraic Geometry (2021) 430-464

10. Variation of singular Kähler-Einstein metrics: Kodaira dimension zero (with Henri Guenancia and Mihai Păun) J. Eur. Math. Soc. (2021)

11. Subharmonicity of direct images and applications (with Frédéric Campana and Mihai Păun) 

12. Variation of singular Kähler-Einstein metrics (with Henri Guenancia and Mihai Păun) J. Reine Angew. Math. 779, 1-36 (2021)

13. Rational curves on compact Kähler manifolds  (with A. Höring) Journal of Differential Geometry, 114 (2020), no. 1, 1-39

14. A decomposition theorem for projective manifolds with nef anticanonical bundle (with A. Höring) Journal of Algebraic Geometry, 28 (2019): 567-597

15. Albanese maps of projective manifolds with nef anticanonical bundles  Ann. Sci. Éc. Norm. Sup. 52 (2019), 1137-1154

16. Kodaira dimension of algebraic fiber spaces over surfaces  Algebraic Geometry 5 (6) 2018, 728-741

17. Ohsawa-Takegoshi extension theorem for compact Kähler manifolds and applications  Complex and Symplectic Geometry, Springer INdAM Series 21, ed. by D. Angella, C. Medori and A. Tomassini (2017), 19-38

18. A general extension theorem for cohomology classes on non reduced analytic spaces (with J.-P. Demailly and S.-I. Matsumura) Sci. China Math. 60 (2017), no. 6, 949–962

19. Kodaira dimension of algebraic fiber spaces over Abelian varieties, (with M. Păun) Invent. Math. 207 (2017), no. 1, pp 345-387

20. Manifolds with nef anticanonical bundle, (with A. Höring) J. Reine Angew. Math. 724 (2017), 203–244

21. Additivity of the approximation functional of currents induced by Bergman kernels C. R. Acad. Sci. Paris, 353 (2015), no.2, pp 117-119

22. On the approximation of Kähler manifolds by algebraic varieties  Math. Annal. 363 (2015), no. 1, pp 393-422

23. Numerical dimension and a Kawamata-Viehweg-Nadel type vanishing theorem on compact Kähler manifolds  Compos. Math. 150 (2014), n.11, pp 1869-1902

24. A remark on compact Kähler manifolds with nef anticanonical bundles and applicaions

25. Les classes de Chern de la cohomologie de Bott-Chern entière  Master’s thesis, Ecole Polytechnique, supervised by Jean-Pierre Demailly

2021-2022: Analyse Fonctionnelle M1

References:  

• Jean-Yves Chemin: Bases d'Analyse Fonctionnelle,  https://www.ljll.math.upmc.fr/~chemin/pdf/4M005_final_W.pdf

• Haïm Brezis: Analyse fonctionnelle, Théorie et applications.

• Haïm Brezis: Functional Analysis, Sobolev Spaces and Partial Differential Equations

• National University of Singapore, Singapore, 30/04/2017-28/05/2017

• Tohuko University, Japan, 10/07/2016-16/07/2016

• FIRAS, Fribourg, 19/06/2016-24/06/2016

• KIAS, Seoul, 30/11/2015-12/12/2015

• FIRAS, Fribourg, 13/09/2015-25/09/2015

• Scuola normale superiore, Pisa, 24/05/2015-30/05/2015