Picture of Yuchen Liu

Yuchen Liu

About me:

I am a Gibbs Assistant Professor in the math department at Yale University. In June 2017, I received my Ph.D. from Princeton University under the supervision of Professor János Kollár.

Together with Sam Payne, Asher Auel, Kalina Mincheva and Max Kutler, I am co-organizing the Yale Algebraic and Tropical Geometry Seminar.

Research Interests

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


Spring 2018: Reflection Groups (MATH 235) at Yale.

Fall 2017: Linear Algebra with Applications (MATH 222) at Yale.

Fall 2017: Foundations of Algebraic Geometry (MATH 619) at Yale.

Spring 2016: Linear Algebra with Applications (MAT 202) at Princeton.

Publications & preprints

Yuchen Liu's papers on arXiv
  1. Birational superrigidity and K-stability of singular Fano complete intersections (joint with Ziquan Zhuang). Preprint, arXiv:1803.08871.
  2. The normalized volume of a singularity is lower semicontinuous (joint with Harold Blum). Submitted, arXiv:1802.09658.
  3. K-stability of cubic threefolds (joint with Chenyang Xu). Submitted, arXiv:1706.01933.
  4. Construction of hyperbolic Horikawa surfaces. Accepted by Ann. Inst. Fourier (Grenoble), arXiv:1702.08143.
  5. Characterization of projective spaces by Seshadri constants (joint with Ziquan Zhuang). Accepted by Math. Z., arXiv:1607.05743.
  6. The volume of singular Kähler-Einstein Fano varieties. Accepted by Compos. Math., arXiv:1605.01034.
  7. Kähler-Einstein metrics and volume minimization (joint with Chi Li). Accepted by Adv. Math., arXiv:1602.05094.
  8. Hyperbolicity of cyclic covers and complements. Accepted by Trans. Amer. Math. Soc., arXiv:1601.07514.
  9. Semi-continuity of complex singularity exponents in singular central fiber cases. Master Thesis, arXiv:1211.1450.