Picture of Yuchen Liu

Yuchen Liu

About me:

I am a Gibbs Assistant Professor in the math department at Yale University. In Spring 2019, I will be a member of the program "Birational Geometry and Moduli Spaces" at MSRI. In June 2017, I received my Ph.D. from Princeton University under the supervision of Professor János Kollár.

Together with Sam Payne, Asher Auel and Kalina Mincheva, I am co-organizing the Yale Algebraic and Tropical Geometry Seminar. We are also co-organizing the BATMOBYLE with organizers from Brown University.

Research Interests

Algebraic geometry -- Fano varieties, K-stability, normalized volumes and Brody hyperbolicity.

Teaching

At Yale

Fall 2018: Reading Course on Algebraic Surfaces

Spring 2018: Reflection Groups (MATH 235)

Fall 2017: Linear Algebra with Applications (MATH 222)

Fall 2017: Foundations of Algebraic Geometry (MATH 619)

At Princeton

Spring 2016: Linear Algebra with Applications (MAT 202)

Publications & preprints

Yuchen Liu's papers on arXiv
  1. A guided tour to normalized volume (joint with Chi Li and Chenyang Xu). Submitted, arXiv:1806.07112.
  2. Birational superrigidity and K-stability of singular Fano complete intersections (joint with Ziquan Zhuang). Submitted, arXiv:1803.08871.
  3. The normalized volume of a singularity is lower semicontinuous (joint with Harold Blum). Submitted, arXiv:1802.09658.
  4. K-stability of cubic threefolds (joint with Chenyang Xu). Submitted, arXiv:1706.01933.
  5. Kähler-Einstein metrics and volume minimization (joint with Chi Li). Accepted by Adv. Math., arXiv:1602.05094.
  6. Hyperbolicity of cyclic covers and complements. Trans. Amer. Math. Soc. 370 (2018), no. 8, 5341-5357, arXiv:1601.07514.
  7. Characterization of projective spaces by Seshadri constants (joint with Ziquan Zhuang). Math. Z. 289 (2018), no. 1-2, 25-38, arXiv:1607.05743.
  8. Construction of hyperbolic Horikawa surfaces. Ann. Inst. Fourier (Grenoble) 68 (2018), no. 2, 541-561, arXiv:1702.08143.
  9. The volume of singular Kähler-Einstein Fano varieties. Compos. Math. 154 (2018), no. 6, 1131-1158, arXiv:1605.01034.

Other writings

  1. Kähler-Einstein metrics and normalized volumes of valuations. Ph.D. Thesis, Princeton University, link.
  2. Semi-continuity of complex singularity exponents in singular central fiber cases. Master Thesis, Peking University, arXiv:1211.1450.