# Welcome to My Homepage!

## WANJUN AI

My chinese name is 艾万君.

I am currently an associate professor in Southwest university (SWU).

I am also the author of LaTeX2HTML — A wordpress plugin making your life easier when write math blog. As a byproduct of learning Laravel, KPr is a website which can push ebooks, such as *mobi* and *azw3*, automatically to your kindle.

Since TeX is a daily must-have writing tool, I've made a report class template (called ustcmb) for preparing math report myself. It supports writing reports in Chinese and English both, and is configured with a color theme based on USTC's transitional color. I believe you can easily adopt to your needs.

You can contact me by the following information.

Address
School of Mathematical Sciences and Statistics,

Southwest University,

TianSheng Road, Beibei District,

Chongqing, 200240, P.R. China

wanjunai(AT)swu(dot)edu(dot)cn

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; Tutor: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), 2019.5-2023.5

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), 2023.6-now

My research interest include:

- Analysis of PDEs
- Differential geometry
- Geometric inequalities

- W. Ai, J. Wang and M. Zhu, The free boundary value problem of α-harmonic maps flow, to appear in Commun. Math. Stat. (2024)
- W. Ai, S-H. Jiang and J. Jost, Variational aspects of the generalized Seiberg-Witten functional, arXiv: 2401.09924 [math.AP]
- W. Ai, L. Lei and M. Zhu, Boundary blow-up analysis for approximate Dirac-harmonic maps into stationary Lorentzian manifolds, to appare in Sci. China Math. ( 2024)
- W. Ai and M. Zhu, The qualitative behavior for approximate Dirac-harmonic maps into stationary Lorentzian manifolds, Sci. China Math. 65(2022), no. 8, 1679---1706. MR4456269
- W. Ai and M. Zhu, Regularity for Dirac-harmonic maps into certain pseudo-Riemannian manifolds, J. Funct. Anal. 279(2020), no. 7, 108633, 28. MR4102160
- W. Ai, C. Song and M. Zhu, The boundary value problem for Yang-Mills-Higgs fields, Calc. Var. Partial Differential Equations 58(2019), no. 4, Paper No. 157, 37. MR3989961
- W. Ai and H. Yin, Neck analysis of extrinsic polyharmonic maps, Ann. Global Anal. Geom. 52(2017), no. 2, 129---156. MR3690012
- W. Ai, The flow of gauge transformations on Riemannian surface with boundary, Commun. Math. Stat. 5(2017), no. 3, 277---316. MR3712514

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

Dissertations- Ai W.-J. Gauge transformation flow on Riemann surfaces and the neck analysis of polyharmonic maps. Phd Thesis, 2017.
- Ai W.-J. Poincaré and Blaschke translative kinematic formulae in the plane. Master thesis, 2012.
- Ai W.-J. Poincaré and Blaschke translative kinematic formulae in the plane. Master Defense, 2012.

- Recommended Books: based on USTC course, recommend books and guide for study.
- USTC Mathematical Plain: A detailed plan of mathematical courses in USTC.

*Complex Analysis**Real Analysis**Advanced Real Analysis**Differential Geometry*

- MathSciNet: Mathematical reviews
- arXiv: An e-print service in several fields including mathematics
- Google: The best search engine in the world
- Google Scholar: I use it to inform me about the latest research relative to my work
- LibGen: The largest and longest running currently openly available collection. A good place to find e-books
- Z-Library: Part of the Z-Library project. The world's largest digital library
- Sci-Hub: The first website in the world to provide mass & public access to research papers, 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*

- 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

- Conway's Game of Life: Implementation by javascript and canvas

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 transplant from mind to mind. There are many ideas in mathematics that may be 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.

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