I am a FWO postdoc researcher at KU Leuven (Mentor Prof. N. Budur). I obtained my Ph.D degree from Purdue University in Aug 2018 (Advisor Prof. D. Arapura). I was a postdoc researcher at Ludwig-Maximilians-Universität München during 09.2018-09.2019 (Mentor Prof. S. Schreieder)

My research centers around Algebraic Geometry and Hodge theory. Currently, I am working on projects about the generic vanishing theorem and its birational application, the assymptotic Hodge theory, nonabelian Hodge theory, and topology of algebraic variety.


Contact:

  • Algebra Section, Celestijnenlaan 200b - box 2400, 3001 Leuven, Belgium

  • feng.hao@kuleuven.be

Education:

  • Ph.D. in Mathematics, Purdue University, West Lafayette, IN, USA, August 2018

  • B.S. in Mathematics, Shandong University, Shandong, China, June 2012

Publications and preprints:

  • $\pi_1$-small divisors and fundamental groups of varieties, to appear IMRN.

  • Equality in the Miyaoka-Yau inequality in the non-general type case, (with S. Schreieder), Journal für die reine und angewandte Mathematik, 775 (2021), 87--115.

  • Holomorphic one-forms without zeros on threefolds, (with S. Schreieder), Geometry & Topology, 25(2021), 409-444.

  • Vanishing theorem for parabolic Higgs bundles, (with D. Arapura and H. Li), Math. Res. Lett., 26 (2019), 1251-1279.

  • Weak bounded negativity conjecture, Proc. Amer. Math. Soc. 147 (2019), 3233-3238.

  • Vanishing theorem for tame harmonic bundles via L2-cohomology, (with Y. Deng), arXiv:1912.02586 (submitted).

  • Generic Vanishing and Holomorphic 1-forms, (with Y. Dutta and Y. Liu), arXiv:2104.07074 (submitted).

  • Limiting Mixed Hodge Theory and Nonabelian Hodge Theory for Nodal Curves, Ph.D Thesis, Purdue University, (2018).