Picture of Yuchen Liu

Yuchen Liu 刘雨晨

About me

I am an Associate 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 CAREER Grant DMS-2237139 and an AT&T Research Fellowship from Northwestern University.

Northwestern Algebraic Geometry Seminar

Northwestern-UIC Complex Geometry Seminar, Apr. 17, 2025

Asymptotics in Complex Geometry, a conference in memory of Steve Zelditch, Mar. 7 -- 10, 2024

Research Interests

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

Teaching

Spring 2025: Algebraic Geometry (MATH 483-2)

Spring 2025: MENU Abstract Algebra (MATH 331-3)

Past Teaching

Publications & preprints

arXiv, Google Scholar, MathSciNet, zbMATH
  1. Hassett--Keel Program in genus four (joint with Kenneth Ascher, Kristin DeVleming, and Xiaowei Wang). Preprint. arXiv:2504.20312.
  2. Non-proportional wall crossing for K-stability (joint with Chuyu Zhou). Submitted. arXiv:2412.15725.
  3. K-moduli with real coefficients (joint with Chuyu Zhou). Submitted. arXiv:2412.15723.
  4. Good moduli spaces for boundary polarized Calabi-Yau surface pairs (joint with Harold Blum). Submitted. arXiv:2407.00850.
  5. Wall-crossing for K-moduli spaces of certain families of weighted projective hypersurfaces (joint with In-Kyun Kim and Chengxi Wang). Submitted. arXiv:2406.07907.
  6. K-stability of special Gushel-Mukai manifolds (joint with Linsheng Wang). Submitted. arXiv:2405.10797.
  7. Moduli of boundary polarized Calabi-Yau pairs (joint with Kenneth Ascher, Dori Bejleri, Harold Blum, Kristin DeVleming, Giovanni Inchiostro, and Xiaowei Wang). Submitted. arXiv:2307.06522.
  8. On the boundedness of singularities via normalized volume (joint with Joaquín Moraga and Hendrik Süß). Submitted. arXiv:2205.12326v4.
  9. K-semistability of log Fano cone singularities (joint with Yueqiao Wu). Accepted by Michigan Math. J.. arXiv:2408.05189.
  10. Irreducible symplectic varieties with a large second Betti number (joint with Zhiyu Liu and Chenyang Xu). Accepted by J. Reine Angew. Math.. arXiv:2410.01566.
  11. K-moduli of Fano threefolds and genus four curves (joint with Junyan Zhao). Accepted by J. Reine Angew. Math.. arXiv:2403.16747.
  12. A note on Kollár valuations (joint with Chenyang Xu). Accepted by Sci. China Math., special issue in memory of Professor Gang Xiao. arXiv:2406.00228.
  13. On K-moduli of quartic threefolds (joint with Hamid Abban, Ivan Cheltsov, Alexander Kasprzyk, and Andrea Petracci). Accepted by Algebr. Geom.. arXiv:2210.14781.
  14. Infinitely many families of Sasaki-Einstein metrics on spheres (joint with Taro Sano and Luca Tasin). Accepted by J. Differential Geom.. arXiv:2203.08468.
  15. Wall crossing for K-moduli spaces of plane curves (joint with Kenneth Ascher and Kristin DeVleming). Proc. Lond. Math. Soc. (3) 128 (2024), no. 6, Paper No. 12615, 113 pp. arXiv:1909.04576.
  16. Convexity of multiplicities of filtrations on local rings (joint with Harold Blum and Lu Qi). Compos. Math. (2024), no. 4, 878-914. arXiv:2208.04902.
  17. ACC for local volumes and boundedness of singularities (joint with Jingjun Han and Lu Qi). J. Algebraic Geom. 32 (2023), no. 3, 519-583. arXiv:2011.06509.
  18. On the Cheltsov-Rubinstein conjecture (joint with Kento Fujita, Hendrik Süß, Kewei Zhang, and Ziquan Zhuang). Birational geometry, Kähler–Einstein metrics and degenerations, 865-883. Springer Proc. Math. Stat., 409, Springer, Cham, 2023. arXiv:1907.02727.
  19. K-stability and birational models of moduli of quartic K3 surfaces (joint with Kenneth Ascher and Kristin DeVleming). Invent. Math. 232 (2023), no. 2, 471-552. arXiv:2108.06848.
  20. K-moduli of curves on a quadric surface and K3 surfaces (joint with Kenneth Ascher and Kristin DeVleming). J. Inst. Math. Jussieu 22 (2023), no. 3, 1251-1291. arXiv:2006.06816.
  21. The existence of the Kähler-Ricci soliton degeneration (joint with Harold Blum, Chenyang Xu, and Ziquan Zhuang). Forum Math. Pi 11 (2023), Paper No. e9, 28 pp. arXiv:2103.15278.
  22. K-stability of Fano threefolds of rank 2 and degree 14 as double covers. Math. Z. 303 (2023), no. 2, Paper No. 38, 9 pp. arXiv:2204.06709.
  23. Optimal destabilization of K-unstable Fano varieties via stability thresholds (joint with Harold Blum and Chuyu Zhou). Geom. Topol. 26 (2022), no. 6, 2507-2564. arXiv:1907.05399.
  24. Openness of K-semistability for Fano varieties (joint with Harold Blum and Chenyang Xu). Duke Math. J. 171 (2022), no. 13, 2753-2797. arXiv:1907.02408.
  25. Finite generation for valuations computing stability thresholds and applications to K-stability (joint with Chenyang Xu and Ziquan Zhuang). Ann. of Math. (2) 196 (2022), no. 2, 507-566. arXiv:2102.09405.
  26. 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.
  27. K-stability of cubic fourfolds. J. Reine Angew. Math. 786 (2022), 55-77. arXiv:2007.14320.
  28. On the sharpness of Tian's criterion for K-stability (joint with Ziquan Zhuang). Nagoya Math. J. 245 (2022), 41-73. arXiv:1903.04719.
  29. 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.
  30. Equivariant K-stability under finite group action (joint with Ziwen Zhu). Internat. J. Math. 33 (2022), no. 1, Paper No. 2250007, 21 pp. arXiv:2001.10557.
  31. 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, 39 pp. arXiv:2011.01895.
  32. 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.
  33. 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.
  34. A guided tour to normalized volume (joint with Chi Li and Chenyang Xu). Geometric analysis—in honor of Gang Tian's 60th birthday, 167-219, Progr. Math., 333, Birkhäuser/Springer, Cham, 2020. arXiv:1806.07112.
  35. K-stability of cubic threefolds (joint with Chenyang Xu). Duke Math. J. 168 (2019), no. 11, 2029-2073. arXiv:1706.01933.
  36. Kähler-Einstein metrics and volume minimization (joint with Chi Li). Adv. Math. 341 (2019), 440-492. arXiv:1602.05094.
  37. Hyperbolicity of cyclic covers and complements. Trans. Amer. Math. Soc. 370 (2018), no. 8, 5341-5357. arXiv:1601.07514.
  38. Characterization of projective spaces by Seshadri constants (joint with Ziquan Zhuang). Math. Z. 289 (2018), no. 1-2, 25-38. arXiv:1607.05743.
  39. Construction of hyperbolic Horikawa surfaces. Ann. Inst. Fourier (Grenoble) 68 (2018), no. 2, 541-561. arXiv:1702.08143.
  40. The volume of singular Kähler-Einstein Fano varieties. Compos. Math. 154 (2018), no. 6, 1131-1158. arXiv:1605.01034.

Other writings

  1. Moduli continuity method in K-stability. Oberwolfach Report (2024).
  2. Moduli of log Calabi-Yau pairs. Oberwolfach Report (2022).
  3. 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.
  4. Appendix to "ACC for minimal log discrepancies of exceptional singularities" by Jingjun Han, Jihao Liu, and V.V. Shokurov. arXiv:1903.04338.
  5. Kähler-Einstein metrics and normalized volumes of valuations. Ph.D. Thesis, Princeton University. Link.
  6. Semi-continuity of complex singularity exponents in singular central fiber cases. Master Thesis, Peking University. arXiv:1211.1450.