My name in Chinese: 张世宇
Email: shiyu123@mail.ustc.edu.cn
I was born in 1999. Currently, I am a fifth-year Ph.D. student in Mathematics at the University of Science and Technology of China (USTC) under the supervision of Professor Xi Zhang, where I completed my B.S. in June 2020.
My research primarily focuses on complex geometry. My knowledge is still quite limited and I'm just learning as I go. Recently, I've recently developed an interest in the generalized Kawamata–Viehweg vanishing theorem and the nonabelian Hodge correspondence.
[5] In preparation.
Based on the ideas developed in the previous paper [2], we can establish the structure theorems for partially semi-positive curvature conditions.
One of the most intriguing implications of this paper is the Hacon-M^ckernan's type question for k-semi-positive Ricci curvature.
Of independent interests, we confirm a question of Ni that a compact K\"ahler manifolds with positive orthogonal Ricci curvature is rationally connected. [4] Compact K\"ahler manifolds with partially semi-positive curvature, (with X. Zhang), arxiv preprint:2504.13155.
We extend the classical Miyaoka-Yau inequality to all minimal K\"ahler klt spaces.
One key is the existence of orbifold modification by Ou for klt spaces.
Our argument is indeed new even for the smooth case. [3] The Miyaoka-Yau inequality on minimal K\"ahler spaces, (with C. Zhang and X. Zhang), arXiv preprint:2503.13365.
The main result is the establishment of a "pseudoeffective" version of Bochner-type theorem, which leads to a splitting of the tangent bundle.
This is a key step of the structure theorems of HSC≥0 for the Kahler case obtained by Professor S. Matsumura recently. [2] On the structure of compact K\"ahler manifolds with nonnegative holomorphic sectional curvature, (with X. Zhang), arXiv preprint:2311.18779v4.
[1] Regularizing property of the twisted conical Kähler-Ricci flow, (with J. Liu and X. Zhang), arxiv preprint.
• 2022F: Analysis 1.
• 2022S: Riemann Surfaces.
• 2021F: Analysis 3.
• 2021S: Analysis 2.
• 2020F: Analysis 1.
• 2020S: Partial differential equations.
• 2019F: Differential geometry of curves and surfaces.
• 2018F: Ordinary differential equations.