Picture of Yuchen Liu

Yuchen Liu 刘雨晨

About me

I am an Assistant Professor in the math department at Northwestern University. Before that, I was a Gibbs Assistant Professor at Yale University and a Visiting Assistant Professor at Princeton University. In 2017, I received my Ph.D. from Princeton University under the supervision of Professor János Kollár.

My research is partially supported by NSF Grant DMS-2148266 (formerly DMS-2001317).

Northwestern Algebraic Geometry Seminar

Special Month On Singularities & K-Stability, University of Utah (virtual)

AIM Workshop (virtual): Moduli problems beyond geometric invariant theory

Research Interests

Algebraic geometry -- Fano varieties, K-stability, moduli spaces, and singularities.


Winter 2022: Algebraic Geometry (MATH 483-2)

Fall 2021: Commutative Algebra (MATH 477-0)

Fall 2021: Abstract Algebra (MATH 330-1)

Past Teaching

Publications & preprints

arXiv, Google Scholar, MathSciNet, zbMATH
  1. K-stability of Fano threefolds of rank 2 and degree 14 as double covers. Submitted. arXiv:2204.06709.
  2. Infinitely many families of Sasaki-Einstein metrics on spheres (joint with Taro Sano and Luca Tasin). Submitted. arXiv:2203.08468.
  3. K-stability and birational models of moduli of quartic K3 surfaces (joint with Kenneth Ascher and Kristin DeVleming). Submitted. arXiv:2108.06848.
  4. The existence of the Kähler-Ricci soliton degeneration (joint with Harold Blum, Chenyang Xu, and Ziquan Zhuang). Submitted. arXiv:2103.15278.
  5. Wall crossing for K-moduli spaces of plane curves (joint with Kenneth Ascher and Kristin DeVleming). Submitted. arXiv:1909.04576.
  6. On the Cheltsov-Rubinstein conjecture (joint with Kento Fujita, Hendrik Süß, Kewei Zhang, and Ziquan Zhuang). Submitted. arXiv:1907.02727.
  7. Finite generation for valuations computing stability thresholds and applications to K-stability (joint with Chenyang Xu and Ziquan Zhuang). Accepted by Ann. of Math.. arXiv:2102.09405.
  8. ACC for local volumes and boundedness of singularities (joint with Jingjun Han and Lu Qi). Accepted by J. Algebraic Geom.. arXiv:2011.06509.
  9. K-stability of cubic fourfolds. Accepted by J. Reine Angew. Math.. arXiv:2007.14320.
  10. K-moduli of curves on a quadric surface and K3 surfaces (joint with Kenneth Ascher and Kristin DeVleming). Accepted by J. Inst. Math. Jussieu. arXiv:2006.06816.
  11. Optimal destabilization of K-unstable Fano varieties via stability thresholds (joint with Harold Blum and Chuyu Zhou). Accepted by Geom. Topol.. arXiv:1907.05399.
  12. Openness of K-semistability for Fano varieties (joint with Harold Blum and Chenyang Xu). Accepted by Duke Math. J.. arXiv:1907.02408.
  13. On the sharpness of Tian's criterion for K-stability (joint with Ziquan Zhuang). Nagoya Math. J. 245 (2022), 41-73. arXiv:1903.04719.
  14. On K-stability of some del Pezzo surfaces of Fano index 2 (joint with Andrea Petracci). Bull. Lond. Math. Soc. 54 (2022), no. 2, 517-525. arXiv:2011.05094.
  15. Openness of uniform K-stability in families of Q-Fano varieties (joint with Harold Blum). Ann. Sci. Éc. Norm. Supér. (4) 55 (2022), no. 1, 1-41. arXiv:1808.09070.
  16. Equivariant K-stability under finite group action (joint with Ziwen Zhu). Internat. J. Math. 33 (2022), no. 1, Paper No. 2250007. arXiv:2001.10557.
  17. On properness of K-moduli spaces and optimal degenerations of Fano varieties (joint with Harold Blum, Daniel Halpern-Leistner, and Chenyang Xu). Selecta Math. (N.S.) 27 (2021), no. 4, Paper No. 73. arXiv:2011.01895.
  18. The normalized volume of a singularity is lower semicontinuous (joint with Harold Blum). J. Eur. Math. Soc. (JEMS) 23 (2021), no. 4, 1225-1256. arXiv:1802.09658.
  19. Birational superrigidity and K-stability of singular Fano complete intersections (joint with Ziquan Zhuang). Int. Math. Res. Not. IMRN 2021, no. 1, 382-401. arXiv:1803.08871.
  20. 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.
  21. K-stability of cubic threefolds (joint with Chenyang Xu). Duke Math. J. 168 (2019), no. 11, 2029-2073. arXiv:1706.01933.
  22. Kähler-Einstein metrics and volume minimization (joint with Chi Li). Adv. Math. 341 (2019), 440-492. arXiv:1602.05094.
  23. Hyperbolicity of cyclic covers and complements. Trans. Amer. Math. Soc. 370 (2018), no. 8, 5341-5357. arXiv:1601.07514.
  24. Characterization of projective spaces by Seshadri constants (joint with Ziquan Zhuang). Math. Z. 289 (2018), no. 1-2, 25-38. arXiv:1607.05743.
  25. Construction of hyperbolic Horikawa surfaces. Ann. Inst. Fourier (Grenoble) 68 (2018), no. 2, 541-561. arXiv:1702.08143.
  26. The volume of singular Kähler-Einstein Fano varieties. Compos. Math. 154 (2018), no. 6, 1131-1158. arXiv:1605.01034.

Other writings

  1. Appendix to "On the optimal volume upper bound for Kähler manifolds with positive Ricci curvature" by Kewei Zhang. Int. Math. Res. Not. IMRN 2022, no. 8, 6135-6156. arXiv:2001.04169.
  2. Appendix to "ACC for minimal log discrepancies of exceptional singularities" by Jingjun Han, Jihao Liu, and V.V. Shokurov. arXiv:1903.04338.
  3. Kähler-Einstein metrics and normalized volumes of valuations. Ph.D. Thesis, Princeton University. Link.
  4. Semi-continuity of complex singularity exponents in singular central fiber cases. Master Thesis, Peking University. arXiv:1211.1450.