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B.S. in Mathematics, Southwest University, China, 2009

M.S. in Mathematics (Advisor: Jiazu Zhou), Southwest University, China, 2012

Ph.D. in Mathematics (Advisor: Jiayu Li & Hao Yin), University of Science and Technology of China, China (USTC), 2017

Postdoc. in Mathematics (Advisor: Miaomiao Zhu), Shanghai Jiao Tong University (SJTU), 2019

Lecturer, in school of mathematics and statistics, Southwest university (SWU), 2019.05 — 2023.05

Visiting Scholar, at Max Planck Institute for Mathematics in the Sciences (MPI-MiS, Host: Jürgen Jost), 2023.04 — 2024.04

Associate Professor, in school of mathematics and statistics, Southwest university (SWU), 2023.06 — now

Visiting Scholar, at Shanghai Center for Mathematical Sciences (SCMS, Host: Qi Ding), 2024.06.01 — 2024.06.30

Visiting Scholar, at Beijing International Center for Mathematical Research (BICMR, Host: Gang Tian), 2024.07.01 — 2024.08.31

Analysis of PDEs, Differential geometry

1. Ai, Wanjun and Liu, Lei and Zhu, Miaomiao, Boundary blow-up analysis for approximate Dirac-harmonic maps into stationary Lorentzian manifolds , Sci. China Math. 68 (2025) , no. 3 , 649--676 MR4868118 DOI: 10.1007/s11425-023-2267-9
2. Ai, Wanjun and Zhu, Miaomiao, The Yang--Mills $\alpha$-Flow over 4-Manifold with Boundary , (2025)
3. Ai, Wanjun and Wang, Jun and Zhu, Miaomiao, The free boundary value problem of $\alpha$-harmonic maps flow , Commun. Math. Stat. (2024) DOI: 10.1007/s40304-024-00399-1
4. Ai, Wanjun and Jiang, Shuhan and Jost, Jürgen, Variational aspects of the generalized Seiberg-Witten functional , Calc. Var. Partial Differential Equations 63 (2024) , no. 7 , Paper No. 178, 27 MR4773605 DOI: 10.1007/s00526-024-02771-z
5. Ai, Wanjun and Zhu, Miaomiao, The qualitative behavior for approximate Dirac-harmonic maps into stationary Lorentzian manifolds , Sci. China Math. 65 (2022) , no. 8 , 1679--1706 MR4456269 DOI: 10.1007/s11425-020-1895-7
6. Ai, Wanjun and Zhu, Miaomiao, Regularity for Dirac-harmonic maps into certain pseudo-Riemannian manifolds , J. Funct. Anal. 279 (2020) , no. 7 , 108633, 28 MR4102160 DOI: 10.1016/j.jfa.2020.108633
7. Ai, Wanjun and Song, Chong and Zhu, Miaomiao, The boundary value problem for Yang-Mills-Higgs fields , Calc. Var. Partial Differential Equations 58 (2019) , no. 4 , Paper No. 157, 37 MR3989961 DOI: 10.1007/s00526-019-1587-z
8. Ai, Wanjun and Yin, Hao, Neck analysis of extrinsic polyharmonic maps , Ann. Global Anal. Geom. 52 (2017) , no. 2 , 129--156 MR3690012 DOI: 10.1007/s10455-017-9551-7
9. Ai, Wanjun, The flow of gauge transformations on Riemannian surface with boundary , Commun. Math. Stat. 5 (2017) , no. 3 , 277--316 MR3712514 DOI: 10.1007/s40304-017-0112-y

For more infomation, you can find me on arXiv, Google Scholar, Research Gate and MathSciNet. My ORCID is Wanjun Ai.

• Complex Analysis
• Real Analysis
• Advanced Real Analysis
• Differential Geometry

• Calculus@sjtu:2018/Autumn. Chap8, Chap9, Midterm, Chap10, Chap11, Finalterm.

• Recommended Books: based on USTC course, recommend books and guide for study.
• USTC Mathematical Plain: A detailed plan of mathematical courses in USTC.
• Cambridge Lecture Notes by Dexter Chua: Comprehensive notes from lectures at Cambridge University.

• Ten commandments on technical presentations by Jaspal Subhlok and others
• The Most Common Habits from more than 200 English Papers written by Graduate Chinese Engineering Students, by Felicia Brittman
• How to write good reference letters

• Seminars: View and add upcoming seminars (login required for adding talks)
• Colloquium: Geometric and Analysis
• Report Generator: Generate LaTeX templates for talks

• MathSciNet: Mathematical reviews
• arXiv: An e-print service in several fields including mathematics
• Google Scholar: I use it to inform me about the latest research relative to my work
• ResearchGate: Academic social network and research sharing platform
• ORCID: My academic profile and publication record

• LibGen: The largest and longest running openly available collection. A good place to find e-books, test the availability
• Z-Library: The world's largest ebook library and article repository, test the availability
• Sci-Hub: The first website in the world to provide mass & public access to research papers, test the availability
• Anna's Archive: The largest open-source library in the world, aggregating content from Library Genesis, Z-Library, and more, test the availability

• Detexify: LaTeX handwritten symbol recognition
• Vim: The ubiquitous text editor
• VimTeX: A vim plugin for editing LaTeX files
• Madoko: A fast markdown processor for writing articles, books and presentations, support PDF/HTML/LaTeX as output formats
• Mendeley: A free reference manager and an academic social network
• MR Lookup: A reference tool for linking, powered by AMS
• MR Lookup script: A javascript write by me, which will change the BibTeX key to Author+Year+Title

• Conway's Game of Life: Interactive cellular automaton simulation
• Project Euler: A website dedicated to the fascinating world of mathematics and programming

It's not mathematics that you need to contribute to. It's deeper than that: how might you contribute to humanity, and even deeper, to the well-being of the world, by pursuing mathematics? Such a question is not possible to answer in a purely intellectual way, because the effects of our actions go far beyond our understanding. We are deeply social and deeply instinctual animals, so much that our well-being depends on many things we do that are hard to explain in an intellectual way. That is why you do well to follow your heart and your passion. Bare reason is likely to lead you astray. None of us are smart and wise enough to figure it out intellectually." [expand ...]

The product of mathematics is clarity and understanding. Not theorems, by themselves. Is there, for example any real reason that even such famous results as Fermat's Last Theorem, or the Poincaré conjecture, really matter? Their real importance is not in their specific statements, but their role in challenging our understanding, presenting challenges that led to mathematical developments that increased our understanding."

The world does not suffer from an oversupply of clarity and understanding (to put it mildly). How and whether specific mathematics might lead to improving the world (whatever that means) is usually impossible to tease out, but mathematics collectively is extremely important."

I think of mathematics as having a large component of psychology, because of its strong dependence on human minds. Dehumanized mathematics would be more like computer code, which is very different. Mathematical ideas, even simple ideas, are often hard to get, but are easy once you get them. Because of this, mathematical understanding does not expand in a monotone direction. Our understanding frequently deteriorates as well. There are several obvious mechanisms of decay. The experts in a subject retire and die, or simply move on to other subjects and forget. Mathematics is commonly explained and recorded in symbolic and concrete forms that are easy to communicate, rather than in conceptual forms that are easy to understand once communicated. Translation in the direction conceptual → concrete and symbolic is much easier than translation in the reverse direction, and symbolic forms often replaces the conceptual forms of understanding. And mathematical conventions and taken-for-granted knowledge change, so older texts may become hard to understand."

In short, mathematics only exists in a living community of mathematicians that spreads understanding and breaths life into ideas both old and new. The real satisfaction from mathematics is in learning from others and sharing with others. All of us have clear understanding of a few things and murky concepts of many more. There is no way to run out of ideas in need of clarification. The question of who is the first person to ever set foot on some square meter of land is really secondary. Revolutionary change does matter, but revolutions are few, and they are not self-sustaining — they depend very heavily on the community of mathematicians."

— By Bill Thurston, from mathoverflow.

Remember that the path from ignorance to knowledge in any subject is not straight and true, but is almost always rather zigzagged. One seems to learn things by a method of successive approximations to the truth. Thus, the hirst attempt to master some of the more difficult theorems in this book is not likely to be completely successful. However, do not give up. Rather, proceed with the study of the exercises and examples and some of the later material, confident that your perseverance will be rewarded with a deeper understanding of the ideas involved."

— By William S. Massey.

In any case, however, I should emphasize that mathematics can only be properly learned by going through and understanding the proofs of the main results in detail and by carrying out exercises and computing examples."

— By Jürgen Jost.