Yuchen Liu 刘雨晨
I am a Gibbs Assistant Professor in the math department at Yale University.
In Spring 2019, I was 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 Ivan Losev 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.
My research is partially supported by NSF Grant DMS-2001317.
Algebraic geometry -- Fano varieties, K-stability, normalized volumes, moduli spaces, and Brody hyperbolicity.
Publications & preprints
, Google Scholar
Equivariant K-stability under finite group action (joint with Ziwen Zhu). Submitted.
Wall crossing for K-moduli spaces of plane curves (joint with Kenneth Ascher and Kristin DeVleming). Submitted.
Optimal destabilization of K-unstable Fano varieties via stability thresholds (joint with Harold Blum and Chuyu Zhou). Submitted.
On the Cheltsov-Rubinstein conjecture (joint with Kento Fujita, Hendrik Süß, Kewei Zhang, and Ziquan Zhuang). Submitted.
Openness of K-semistability for Fano varieties (joint with Harold Blum and Chenyang Xu). Submitted.
On the sharpness of Tian's criterion for K-stability (joint with Ziquan Zhuang). Submitted.
Openness of uniform K-stability in families of Q-Fano varieties (joint with Harold Blum). Accepted by
Ann. Sci. Éc. Norm. Supér..
The normalized volume of a singularity is lower semicontinuous (joint with Harold Blum).
Accepted by J. Eur. Math. Soc. (JEMS). arXiv:1802.09658.
Birational superrigidity and K-stability of singular Fano complete intersections (joint with Ziquan Zhuang). Accepted by Int. Math. Res. Not. IMRN.
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.
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.