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Contact Information

  • Email: junyan.cao@unice.fr ; 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

Positions and Education

  • 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

Reserach

ANR Karmapolis with Benoît Cadorel, Ya Deng and Henri Guenancia (project coordinator) .

Publications

  1. Curvature formula for direct images of twisted relative canonical bundles endowed with a singular metric (with Henri Guenancia and Mihai Păun)

  2. On extension of pluricanonical forms defined on the central fiber of a Kähler family (with Mihai Păun)

  3. On the Ohsawa-Takegoshi extension theorem (with Mihai Păun)

  4. Projective klt pairs with nef anti-canonical divisor (with Frédéric Campana and Shin-Ichi Matsumura)

  5. Variation of singular Kähler-Einstein metrics: Kodaira dimension zero (with Henri Guenancia and Mihai Păun)

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

  7. Variation of singular Kähler-Einstein metrics (with Henri Guenancia and Mihai Păun)

  8. Rational curves on compact Kähler manifolds (with Andreas Höring) Journal of Differential Geometry

  9. A decomposition theorem for projective manifolds with nef anticanonical bundle (with Andreas Höring) Journal of Algebraic Geometry

  10. Albanese maps of projective manifolds with nef anticanonical bundles Annales Scientifiques de l'École Normale Supérieure

  11. Kodaira dimension of algebraic fiber spaces over surfaces

  12. 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

  13. A general extension theorem for cohomology classes on non reduced analytic spaces (with Jean-Pierre Demailly and Shin-Ichi Matsumura) Sci. China Math. 60 (2017), no. 6, 949–962

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

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

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

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

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

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

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

Teaching

2021-2022: Analyse Fonctionnelle M1

References:

Visits

  • 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