I am a Gibbs Assistant Professor in the math department at Yale University.
In Spring 2019, I will be 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
Together with Sam Payne, Asher Auel
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.
Algebraic geometry -- Fano varieties, K-stability, normalized volumes and Brody hyperbolicity.
Publications & preprints
Yuchen Liu's papers on arXiv
A guided tour to normalized volume (joint with Chi Li and Chenyang Xu). Submitted,
Birational superrigidity and K-stability of singular Fano complete intersections (joint with Ziquan Zhuang). Submitted,
The normalized volume of a singularity is lower semicontinuous (joint with Harold Blum).
K-stability of cubic threefolds (joint with Chenyang Xu). Submitted,
Kähler-Einstein metrics and volume minimization (joint with Chi Li). Accepted by Adv. Math.,
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.
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,