Ya Deng's Homepage 


Chargé de Recherche au CNRS
Institut Élie Cartan de Lorraine
Université de Lorraine
Email: ya.deng@math.cnrs.fr  

My research subjects contain complex algebraic-analytic geometry, complex hyperbolicity, non-abelian Hodge theories in both Archimedean and non-Archimedean settings, Nevanlinna theory, and the interplay among them. My current interest is harmonic mapping to Euclidean buildings, linear Shafarevich conjecture, hyperbolicity of algebraic varieties via representation of fundamental groups.

Brief CV

  1. Big Picard theorems and algebraic hyperbolicity for varieties admitting a variation of Hodge structures. To appear in L'Épijournal de Géométrie Algébrique arXiv:2001.04426 Abstract Oberwolfach report

  2. A characterization of complex quasi-projective manifolds uniformized by unit balls. (with an appendix written jointly with Benoît Cadorel). To appear in Math. Ann arXiv:2006.16178 Abstract

  3. 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
  4. 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
  5. On the Diverio-Trapani ConjecturearXiv:1703.07560 . Ann. Scient. Éc. Norm. Sup. 4 e série, t. 53, 2020, p. 787 à 814.  link   Abstract
  6. 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
  7. Applications of the Ohsawa-Takegoshi Extension Theorem to Direct Image Problems. Int. Math. Res. Not. IMRN, rnaa018 Abstract

  8. Transcendental morse inequality and generalized Okounkov bodies algebraic geometry. Algebraic Geometry 4 (2) (2017) 177–202. Link Abstract
  9. Simpson correspondence for semistable Higgs bundles over Kähler manifolds. hal-02391629 . Pure and Applied Mathematics Quarterly Volume 17, Number 5, 1899-1911, 2021. Link  Abstract

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

  1. Hyperbolicity and fundamental groups of complex quasi-projective varieties. (joint work with Benoit Cadorel and Katsutoshi Yamanoi) arXiv:2212.12225 Abstract

  2. Representations of fundamental groups and logarithmic symmetric differential forms. (joint work with D. Brotbek, G. Daskalopoulos and C. Mese) arXiv:2206.11835 Abstract

  3. On the nilpotent orbit theorem of complex variation of Hodge structures. arXiv:2203.04266 Abstract

  4. Picard hyperbolicity for manifolds admitting nilpotent harmonic bundles. (joint work with Benoît Cadorel). arXiv:2107.07550 Abstract

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

  6. Vanishing theorem for tame harmonic bundles via \(L^2\)-cohomology. (joint work with Feng HAO) arXiv:1912.02586 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 12. 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

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

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

ANR JCJC Grant: Kähler manifolds with non-positive curvature : families and special subvarieties. 2021-2025 (Homepage)

Members: Henri Guenancia (CNRS-Toulouse, project coordinator), Junyan Cao (Nice), Benoit Cadorel (Nancy), Ya Deng (CNRS-Nancy)

Séminaire de géométrie complexe a l'IECL Lien.