Hi, my name is Yunsong Wei. Welcome to my homepage.

I am a PhD candidate at the Chinese University of Hong Kong, under the supervision of Professor Naichung Conan Leung. I deeply appreciate the valuable guidance and support provided by Prof. Leung during my studies. I earned my M.Phil from the same institution in 2022. I completed my B.S. in Mathematics at the University of Chinese Academy of Sciences in 2020, where I was fortunate to be mentored by Professor Baohua Fu. 

Here is my CV.

E-mail: weiyunsong@link.cuhk.edu.hk

Research

Intersection of twisted cotangent bundles and symplectic duality (2025), (with Conan Naichung Leung),  (arXiv: 2510.19259), PhD Thesis.

• We observe that numerous symplectic resolutions can be expressed as the intersections of twisted cotangent bundles, and their dual symplectic resolutions can be derived from intersections of S-dual twisted cotangent bundles. We determine the collection of fixed points for certain intersections which are Poisson slices.

Markov dynamical systems, evolutionary social networks and applications to graph theory (2025), (with Yujie Fu) 

• This paper applies the ideas from geometry to the study of random dynamical systems from a categorical perspective. Categories, quotients and invariants of Markov dynamical systems are defined. Then we apply these concepts from Markov dynamical systems to characterize graphs, offering new evolutionary explanations for balanced graphs, Eulerian graphs and the rank of the adjacent matrices. 

Invariant algebraic D-modules over affine algebraic groups (2024). (arXiv: 2505.12755)

• The analytic category of D-modules and algebraic category of D-modules are not equivalent on affine varieties. In this paper, we classify invariant algebraic D-modules over unipotent algebraic groups and some solvable algebraic groups. 

Diagonal orbits in the wonderful compactification (2022), (arXiv: 2505.12749), MPhil Thesis (Slides).

• We construct the family of closures of the Steinberg fiber in the De Concini-Procesi compactification and examine the limit of this family, showing that the limit is a union of He-Lusztig's G-stable pieces.

Talks

Feb 27, 2025, MIST: Mathematics Inspired by String Theory 2025, Institute of Mathematical Sciences, CUHK, Hong Kong 

Teaching

Teaching Assistant

2025 Spring: MMAT5540 Advanced Geometry

2024 Fall: MMAT5510 Foundation of Advanced Mathematics

2024 Spring: MATH1030 Linear Algebra I

2023 Fall: MATH1510 Calculus for Engineers

2023 Spring: MATH2060 Mathematical Analysis II

2022 Fall: MATH2020 Advanced Calculus II

2021 Fall: MATH1510 Calculus for Engineers; MATH 1010 University Mathematics

Micellaneous

AWARDS

Honorable Mentions, Alibaba Math Contest 2022, Ranked 30th, awards 5000 USD

Links

Conway's Soldiers 

tikzcd-editor 

I also like sketching.