Ya DENG's homepage

Contact information

Institut des Hautes Études Scientifiques
Office: 0S4
Telephone: +(33) 01 60 92 66 47
Email: deng@ihes.fr  

My current research lies on complex algebraic-analytic geometry, complex hyperbolicity, Hodge theory and the interplay among them. Recently I became interested in arithmetic geometry and o-minimality (e.g. applications to variational Hodge theory and hyperbolicity).

Brief CV

  1. On the hyperbolicity of base spaces for maximal variational families of smooth projective varieties. (with an appendix by Dan Abramovich).  arXiv:1806.01666 To appear in Journal of the European Mathematical Society (JEMS). Abstract
  2. Kobayashi hyperbolicity of the complements of general hypersurfaces of high degrees.  (joint work with Damian Brotbek ),   arXiv:1804.01719.  Geometric And Functional Analysis (GAFA), June 2019, Volume 29, Issue 3, pp 690–750.  link  Abstract
  3. On the Diverio-Trapani ConjecturearXiv:1703.07560 . Ann. Scient. Éc. Norm. Sup. 4 e série, t. 53, 2020, p. 787 à 814.  link   Abstract
  4. On the positivity of the logarithmic cotangent bundle. (joint work with Damian Brotbek ) arXiv:1712.09887. Annales de l'Institut Fourier, Volume 68 (2018) no. 7, p. 3001-3051 (en l'honneur du professeur Jean-Pierre Demailly). link Abstract
  5. Applications of the Ohsawa-Takegoshi Extension Theorem to Direct Image Problems. Int. Math. Res. Not. IMRN, rnaa018 Abstract

  6. Transcendental morse inequality and generalized Okounkov bodies algebraic geometry. Algebraic Geometry 4 (2) (2017) 177–202. Link Abstract
  7. Simpson correspondence for semistable Higgs bundles over Kähler manifolds. hal-02391629 . To appear in Pure and Applied Mathematics Quarterly Abstract

  8. Kobayashi measure hyperbolicity for singular directed varieties of general type. Comptes Rendus Mathématique, Volume 354, Issue 9, (2016), Pages 920-924. Link Abstract

  1. A characterization of complex quasi-projective manifolds uniformized by unit balls. (with an appendix written jointly with Benoît Cadorel). arXiv:2006.16178 Abstract

  2. Big Picard theorem and algebraic hyperbolicity for varieties admitting a variation of Hodge structures. arXiv:2001.04426 Abstract

  3. Picard theorems for moduli spaces of polarized varieties. (joint work with S. Lu, R. Sun and K. Zuo) arXiv:1911.02973 Abstract

  4. Vanishing theorem for tame harmonic bundles via \(L^2\)-cohomology. (joint work with Feng HAO) arXiv:1912.02586 Abstract

  5. Hyperbolicity of coarse moduli spaces and isotriviality for certain families. arXiv:1908.08372 Abstract

  6. Hyperbolicity of bases of log Calabi-Yau families. arXiv:1901.04423 hal-02266744 Abstract

Unpublished preprints
  1. Big Picard theorem for moduli spaces of polarized manifolds. arXiv:1912.11442. Part of this preprint has been merged into Preprint 10. Abstract

  2. Pseudo Kobayashi hyperbolicity of base spaces of families of minimal projective manifolds with maximal variation. arXiv:1809.05891 This preprint has been merged into Publication 1. Abstract

 Le corps d'Okounkov généralisé et des problèmes liés à l'hyperbolicité et l'image directe. Hal link.           Defended in 26 June 2017 at Grenoble.

With Junyan Cao and Mingchen Xia, we are organizing a complex geometry online seminar (homepage).