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) and the Alfred P. Sloan Foundation.

Northwestern Algebraic Geometry Seminar

Northwestern-UIC Complex Geometry Seminar, Oct. 3, 2022

Algebraic geometry and cohomology in mixed characteristic, May. 15 -- 19, 2023

AIM Workshop: Developments in moduli problems, Feb. 27 -- Mar. 3, 2023

Around Complex Geometry, UIC, Apr. 21 -- 23, 2023

Research Interests

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

Teaching

Winter 2023: Abstract Algebra (MATH 330-2)

Fall 2022: Abstract Algebra (MATH 330-1)

Fall 2022: Multivariable Differential Calculus for Engineering (MATH 228-1)

Past Teaching

Publications & preprints

arXiv, Google Scholar, MathSciNet, zbMATH
  1. On K-moduli of quartic threefolds (joint with Hamid Abban, Ivan Cheltsov, Alexander Kasprzyk, and Andrea Petracci). Submitted. arXiv:2210.14781v2.
  2. On the boundedness of singularities via normalized volume (joint with Joaquín Moraga and Hendrik Süß). Submitted. arXiv:2205.12326v4.
  3. Convexity of multiplicities of filtrations on local rings (joint with Harold Blum and Lu Qi). Submitted. arXiv:2208.04902.
  4. Infinitely many families of Sasaki-Einstein metrics on spheres (joint with Taro Sano and Luca Tasin). Submitted. arXiv:2203.08468.
  5. Wall crossing for K-moduli spaces of plane curves (joint with Kenneth Ascher and Kristin DeVleming). Submitted. arXiv:1909.04576.
  6. ACC for local volumes and boundedness of singularities (joint with Jingjun Han and Lu Qi). Accepted by J. Algebraic Geom.. arXiv:2011.06509.
  7. On the Cheltsov-Rubinstein conjecture (joint with Kento Fujita, Hendrik Süß, Kewei Zhang, and Ziquan Zhuang). Birational Geometry, Kähler–Einstein Metrics and Degenerations. Springer Proceedings in Mathematics & Statistics, vol 409. Springer, Cham, 2023. arXiv:1907.02727.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. K-stability of cubic fourfolds. J. Reine Angew. Math. 786 (2022), 55-77. arXiv:2007.14320.
  17. On the sharpness of Tian's criterion for K-stability (joint with Ziquan Zhuang). Nagoya Math. J. 245 (2022), 41-73. arXiv:1903.04719.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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.
  23. 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.
  24. K-stability of cubic threefolds (joint with Chenyang Xu). Duke Math. J. 168 (2019), no. 11, 2029-2073. arXiv:1706.01933.
  25. Kähler-Einstein metrics and volume minimization (joint with Chi Li). Adv. Math. 341 (2019), 440-492. arXiv:1602.05094.
  26. Hyperbolicity of cyclic covers and complements. Trans. Amer. Math. Soc. 370 (2018), no. 8, 5341-5357. arXiv:1601.07514.
  27. Characterization of projective spaces by Seshadri constants (joint with Ziquan Zhuang). Math. Z. 289 (2018), no. 1-2, 25-38. arXiv:1607.05743.
  28. Construction of hyperbolic Horikawa surfaces. Ann. Inst. Fourier (Grenoble) 68 (2018), no. 2, 541-561. arXiv:1702.08143.
  29. 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.