A picture from complex geometry

Kewei Zhang 张科伟

kwzhang at bnu dot edu dot cn | kwzhang at pku dot edu dot cn

I am a professor at Beijing Normal University.

I was a postdoc at BICMR during 2019-2021.

I completed my Ph.D. in 2019 at Peking University, China.

I was also a visiting student at the University of Maryland during 2017-2018.

My research interests include complex geometry, algebraic geometry, and geometric PDE.

Publications and Preprints

C. Li, M. Miao, K. Zhang, The sharp volume gap for Kähler manifolds with positive Ricci curvature, arXiv:2608.08193, 2026, preprint.
T. Darvas, K. Zhang, A YTD correspondence for constant scalar curvature metrics, arXiv:2509.15173, 2025, preprint.
K. Zhang, Quantized volume comparison for Fano manifolds, arXiv:2503.16766, Proc. Amer. Math. Soc. 153 (2025), no. 10, 4379-4385.
K. Zhang, Reduced delta invariant and Kähler-Einstein metrics, Peking Math. J. (2024), published version.
J. Chu, F. Wang, K. Zhang, The rigidity of eigenvalues on Kähler manifolds with positive Ricci lower bound, arXiv:2401.15830, J. Reine Angew. Math. 820 (2025), 213-233.
K. Zhang, The Ricci iteration towards cscK metrics, arXiv:2311.15524, Adv. Math. 475 (2025), Paper No. 110340, 29 pp.
T. Darvas, R. Reboulet, D. Witt Nyström, M. Xia, K. Zhang, Transcendental Okounkov bodies, arXiv:2309.07584, J. Differential Geom. 132 (2026), no. 1, 135-178.
T. Darvas, M. Xia, K. Zhang, A transcendental approach to non-Archimedean metrics of pseudoeffective classes, arXiv:2302.02541, Comment. Math. Helv. 100 (2025), no. 2, 269-322.
T. Darvas, K. Zhang, Twisted Kähler-Einstein metrics in big classes, arXiv:2208.08324, Comm. Pure Appl. Math. 77 (2024), no. 12, 4289-4327.
Y. Ji, Y. A. Rubinstein, K. Zhang, Eguchi-Hanson metrics arising from Kähler-Einstein edge metrics, arXiv:2111.00652, J. Topol. Anal. (2024), doi.
K. Zhang, Filtrations and Chow stability revisited, 2021, English translation of my Chinese article: Acta Math. Sinica (Chinese Ser.) 65 (2022), no. 6, 1033-1044.
K. Zhang, A quantization proof of the uniform Yau-Tian-Donaldson conjecture, arXiv:2102.02438, J. Eur. Math. Soc. 26 (2024), no. 12, 4763-4778.
K. Zhang, Valuative invariants with higher moments, arXiv:2012.04856, J. Geom. Anal. 32 (2022), no. 1, Paper No. 10, 33 pp.
Y. A. Rubinstein, G. Tian, K. Zhang, Basis divisors and balanced metrics, arXiv:2008.08829, J. Reine Angew. Math. 778 (2021), 171-218.
Y. A. Rubinstein, K. Zhang, Angle deformation of Kähler-Einstein edge metrics on Hirzebruch surfaces, arXiv:2011.12666, Pure Appl. Math. Q. 18 (2022), no. 1, 343-366.
K. Zhang, Continuity of delta invariants and twisted Kähler-Einstein metrics, arXiv:2003.11858, Adv. Math. 388 (2021), Paper No. 107888, 25 pp.
K. Zhang, C. Zhou, Delta invariants of projective bundles and projective cones of Fano type, arXiv:2003.06839, Math. Z. 300 (2022), no. 1, 179-207.
K. Zhang, On the optimal volume upper bound for Kähler manifolds with positive Ricci curvature (with an appendix by Y. Liu), arXiv:2001.04169, Int. Math. Res. Not. IMRN 2022, no. 8, 6135-6156.
K. Zhang, Some refinements of the partial C⁰ estimate, arXiv:1911.11328, Anal. PDE 14 (2021), no. 7, 2307-2326.
K. Fujita, Y. Liu, H. Süss, K. Zhang, Z. Zhuang, On the Cheltsov-Rubinstein conjecture, arXiv:1907.02727, Springer Proc. Math. Stat. 409, Springer, Cham, 2023, 865-883.
Y. A. Rubinstein, K. Zhang, Small angle limits of Hamilton's footballs, arXiv:1905.00865, Bull. Lond. Math. Soc. 52 (2020), no. 1, 189-199.
I. Cheltsov, K. Zhang, Delta invariants of smooth cubic surfaces, arXiv:1807.08960, Eur. J. Math. 5 (2019), 729-762.
I. Cheltsov, Y. A. Rubinstein, K. Zhang, Basis log canonical thresholds, local intersection estimates, and asymptotically log del Pezzo surfaces, arXiv:1807.07135, Selecta Math. (N.S.) 25 (2019), Art. 34, 36 pp.

Notes/Papers Generated by AI

The following documents grew out of my conversations with ChatGPT Pro. I only claim 5.9% of the credit here. Please check the correctness carefully before citing any result below.

ChatGPT 5.6, Upper Bounds for Tian's Alpha Invariant of Smooth Fano Manifolds, notes.
ChatGPT 5.6, The Second-Volume Problem for Positive Einstein Four-Manifolds, notes.
ChatGPT 5.5, Okounkov bodies and Seshadri constants for blow-ups along a smooth subvariety, preprint.

Survey Articles

K. Zhang, The optimal exponent of certain Moser-Trudinger type inequalities on projective manifolds, preprint, Surveys in Geometric Analysis 2021, Science Press Beijing.
K. Zhang, Stability threshold and canonical metrics, preprint, Surveys in Geometric Analysis 2020, Science Press Beijing.
K. Zhang, The greatest Ricci lower bound and stability threshold, available here, Surveys in Geometric Analysis 2019, Science Press Beijing.

Notes and Slides

A quantization approach to the cscK problem, 2025, slides.
Analytic thresholds, canonical metrics and Okounkov bodies, 2024, slides.
The Ricci iteration towards cscK metrics, 2023, slides.
Convex bodies associated to Kähler manifolds, 2023, slides.
A pluripotential proof of the uniform YTD conjecture, 2022, slides.
Lectures on the quantization proof of the uniform YTD conjecture, 2022, slides.
The delta invariants of projective bundles, 2020, draft.
Bounding the volume of Kähler manifolds with positive Ricci curvature, 2019, draft.
A remark on alpha_G invariant, 2019, notes.
Stability thresholds of Fano T-varieties of complexity one, 2018, draft.

Teaching

Complex Geometry, Summer School of BICMR, 2021.
Calculus, undergraduate course at BNU, 2022.
Complex Analysis, undergraduate course at BNU, 2023.
Undergraduate Algebraic Geometry, undergraduate course at BNU, 2023.
Introduction to Riemann Surfaces, undergraduate course at BNU, 2024.

Links

Publications and Preprints

Notes/Papers Generated by AI

Survey Articles

Notes and Slides

Teaching