Zheng, Renpeng

PhD Student

University of Nottingham

Renpeng.Zheng <at> Nottingham.ac.uk

Supervised by Hamid Abban and Johannes Hofscheier

郑（ zhèng ）仁（ rén ）鹏（ péng ）

I am working on birational and complex algebraic geometry, mainly focusing on K-stability. I am also interested in geometric shapes encoded by combinatorics, especially toric and spherical varieties.

My newest paper is [Zheng26] Zheng (2026)
K-stability of Q-Fano spherical varieties via compatible divisors, where we find a special ℚ-divisor of a polarised spherical variety.

Education

2027: (Expected) PhD in Pure Mathematics (supervised by Hamid Abban and Johannes Hofscheier), University of Nottingham, UK
2022: MSc in Pure Mathematics (supervised by Jonathan Lai), Imperial College London, UK
2021: BSc in Mathematics and Applied Mathematics, The Chinese University of Hong Kong, Shenzhen, China

Research

Publications / Preprints

Abstracts

[Zheng26]

K-stability of Q-Fano spherical varieties via compatible divisors (2026), at Annales de l’Institut Fourier (to appear), arXiv, .

Abstract

We study the K-stability of ℚ-Fano spherical varieties using compatible divisors. More precisely, if the ℚ-Fano variety, with a reductive group action, has an open Borel subgroup orbit, then there is a unique anticanonical ℚ-divisor computing the equivariant stability threshold. This ℚ-divisor is invariant under the Borel subgroup action, and it characterizes the K-stability of a ℚ-Fano spherical variety.

@article{zheng2026kstabilityqfanosphericalvarieties,
  title={K-stability of Q-Fano Spherical Varieties via Compatible Divisors}, 
  author={Zheng, Renpeng},
  year={2026},
  journaltitle={Annales de l’Institut Fourier (To appear)},
  doi={},
  pages={},
  volume={}
}

Conferences / Seminars

“K-stability of Q-Fano spherical varieties via compatible divisors” (Jun 2026), Junior Algebraic geometry Warwick Seminar, University of Warwick, Coventry, UK. On [Zheng26] Zheng (2026)
K-stability of Q-Fano spherical varieties via compatible divisors.
“K-stability of Q-Fano spherical varieties via compatible divisors” (Jun 2026), Algebraic Geometry Seminar, Kyoto University, Kyoto, Japan. On [Zheng26] Zheng (2026)
K-stability of Q-Fano spherical varieties via compatible divisors.

Posters / Interactive Media

Teaching and Marking

University of Nottingham (Teaching Affiliate and Demonstrator)

2024-2025

MATH1101 Core Mathematics (Full Year UK) - Demonstration.
MATH2102 Real Analysis (Spring UK) - Marking.

2025-2026

MATH2102 Real Analysis (Autumn UK) - Marking.