Picture of Yuchen Liu

Yuchen Liu 刘雨晨

About me:

I am a Gibbs Assistant Professor in the math department at Yale University. In Spring 2019, I was 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.

For the academic year 2020--2021, I will be a Visiting Assistant Professor at Princeton University. Starting from Fall 2021, I will be a Tenure-Track Assistant Professor at Northwestern University.

Together with Ivan Losev 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.

My research is partially supported by NSF Grant DMS-2001317.

Research Interests

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


At Yale

Spring 2020: Discrete Mathematics (MATH 244)

Fall 2019: Linear Algebra with Applications (MATH 222)

Fall 2019: Foundations of Algebraic Geometry (MATH 619)

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

arXiv, Google Scholar
  1. K-stability of cubic fourfolds. Preprint. arXiv:2007.14320.
  2. K-moduli of curves on a quadric surface and K3 surfaces (joint with Kenneth Ascher and Kristin DeVleming). Submitted. arXiv:2006.06816.
  3. Equivariant K-stability under finite group action (joint with Ziwen Zhu). Submitted. arXiv:2001.10557.
  4. Wall crossing for K-moduli spaces of plane curves (joint with Kenneth Ascher and Kristin DeVleming). Submitted. arXiv:1909.04576.
  5. Optimal destabilization of K-unstable Fano varieties via stability thresholds (joint with Harold Blum and Chuyu Zhou). Submitted. arXiv:1907.05399.
  6. On the Cheltsov-Rubinstein conjecture (joint with Kento Fujita, Hendrik Süß, Kewei Zhang, and Ziquan Zhuang). Submitted. arXiv:1907.02727.
  7. Openness of K-semistability for Fano varieties (joint with Harold Blum and Chenyang Xu). Submitted. arXiv:1907.02408.
  8. On the sharpness of Tian's criterion for K-stability (joint with Ziquan Zhuang). Accepted by Nagoya Math. J.. arXiv:1903.04719.
  9. Openness of uniform K-stability in families of Q-Fano varieties (joint with Harold Blum). Accepted by Ann. Sci. Éc. Norm. Supér.. arXiv:1808.09070.
  10. The normalized volume of a singularity is lower semicontinuous (joint with Harold Blum). Accepted by J. Eur. Math. Soc. (JEMS). arXiv:1802.09658.
  11. Birational superrigidity and K-stability of singular Fano complete intersections (joint with Ziquan Zhuang). Accepted by Int. Math. Res. Not. IMRN. arXiv:1803.08871.
  12. A guided tour to normalized volume (joint with Chi Li and Chenyang Xu). Geometric analysis, 167-219, Progr. Math., 333, Birkhäuser/Springer, Cham, 2020. arXiv:1806.07112.
  13. K-stability of cubic threefolds (joint with Chenyang Xu). Duke Math. J. 168 (2019), no. 11, 2029-2073. arXiv:1706.01933.
  14. Kähler-Einstein metrics and volume minimization (joint with Chi Li). Adv. Math. 341 (2019), 440-492. arXiv:1602.05094.
  15. Hyperbolicity of cyclic covers and complements. Trans. Amer. Math. Soc. 370 (2018), no. 8, 5341-5357. arXiv:1601.07514.
  16. Characterization of projective spaces by Seshadri constants (joint with Ziquan Zhuang). Math. Z. 289 (2018), no. 1-2, 25-38. arXiv:1607.05743.
  17. Construction of hyperbolic Horikawa surfaces. Ann. Inst. Fourier (Grenoble) 68 (2018), no. 2, 541-561. arXiv:1702.08143.
  18. 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.