Yuchen Liu 刘雨晨
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
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
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)
Publications & preprints
K-stability of Fano threefolds of rank 2 and degree 14 as double covers. Submitted.
Infinitely many families of Sasaki-Einstein metrics on spheres (joint with Taro Sano and Luca Tasin). Submitted.
K-stability and birational models of moduli of quartic K3 surfaces (joint with Kenneth Ascher and Kristin DeVleming). Submitted.
The existence of the Kähler-Ricci soliton degeneration (joint with Harold Blum, Chenyang Xu, and Ziquan Zhuang). Submitted.
Wall crossing for K-moduli spaces of plane curves (joint with Kenneth Ascher and Kristin DeVleming). Submitted.
On the Cheltsov-Rubinstein conjecture (joint with Kento Fujita, Hendrik Süß, Kewei Zhang, and Ziquan Zhuang). Submitted.
Finite generation for valuations computing stability thresholds and applications to K-stability (joint with Chenyang Xu and Ziquan Zhuang). Accepted by Ann. of Math..
ACC for local volumes and boundedness of singularities (joint with Jingjun Han and Lu Qi). Accepted by J. Algebraic Geom..
K-stability of cubic fourfolds. Accepted by
J. Reine Angew. Math..
K-moduli of curves on a quadric surface and K3 surfaces (joint with Kenneth Ascher and Kristin DeVleming). Accepted by
J. Inst. Math. Jussieu.
Optimal destabilization of K-unstable Fano varieties via stability thresholds (joint with Harold Blum and Chuyu Zhou). Accepted by
Openness of K-semistability for Fano varieties (joint with Harold Blum and Chenyang Xu). Accepted by Duke Math. J..
On the sharpness of Tian's criterion for K-stability (joint with Ziquan Zhuang).
Nagoya Math. J. 245 (2022), 41-73.
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.
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.
Equivariant K-stability under finite group action (joint with Ziwen Zhu).
Internat. J. Math. 33 (2022), no. 1, Paper No. 2250007.
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.
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.
Birational superrigidity and K-stability of singular Fano complete intersections (joint with Ziquan Zhuang). Int. Math. Res. Not. IMRN 2021, no. 1, 382-401.
A guided tour to normalized volume (joint with Chi Li and Chenyang Xu). Geometric analysis, 167-219,
Progr. Math., 333, Birkhäuser/Springer, Cham, 2020.
K-stability of cubic threefolds (joint with Chenyang Xu). Duke Math. J.
168 (2019), no. 11, 2029-2073.
Kähler-Einstein metrics and volume minimization (joint with Chi Li). Adv. Math.
341 (2019), 440-492.
Hyperbolicity of cyclic covers and complements.
Trans. Amer. Math. Soc. 370 (2018), no. 8, 5341-5357.
Characterization of projective spaces by Seshadri constants (joint with Ziquan Zhuang).
Math. Z. 289 (2018), no. 1-2, 25-38. arXiv:1607.05743.
Construction of hyperbolic Horikawa surfaces.
Ann. Inst. Fourier (Grenoble) 68 (2018), no. 2, 541-561.
The volume of singular Kähler-Einstein Fano varieties. Compos. Math. 154
(2018), no. 6, 1131-1158. arXiv:1605.01034.
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.
Appendix to "ACC for minimal log discrepancies of exceptional singularities" by Jingjun Han, Jihao Liu, and V.V. Shokurov.
Kähler-Einstein metrics and normalized volumes of valuations. Ph.D. Thesis, Princeton University.
Semi-continuity of complex singularity exponents in singular central fiber cases. Master Thesis, Peking University.