ABOUT ME 我的简介

I am Jinghao Xu, with Zhihu username 笑颜之花. I am currently an undergraduate student majoring in mathematics, with academic interests leaning toward topology-related geometry. I have studied topics of Geometric Topology and have written notes and surveys such as the Triangulation Conjecture (English Version) and the Poincaré Conjecture (English Version). My studies have broadly covered homology theory, differential manifolds, and Riemannian geometry. In 2025, I participated in the S.-T.Yau College Student Mathematics Contest on Geometry and Topology, where I received an Honorable Mention award.

My personal motto is: “Be your own lifelong liberal arts mentor.” As a result, I have explored a wide range of interests, including playing the harmonica, wound dressing, computer repair, swimming, sewing, and haircutting—though I am not particularly skilled in any of them. At present, I am preparing to practice the piano, and in the future, I plan to study electrical circuits and work on small electronics projects. I also greatly admire the works of some 3D modelers, as 3D animation can visualize geometric transformations—for example, the works of 璐十二 on Bilibili. I hope to acquire such skills myself to develop a more solid geometric intuition.

Recently, I’m proud to have filmed a whole series of graduate standard Algebraic Topology course (taught in Chinese) in summer 2025, which can be viewed at Bilibili.

Now I’m writing my undergraduate thesis themed “Hyperbolization problem on the non-trangulable manifolds”. This theme is based on the fact that “all the triangulable manifolds can be hyperbolized”, i.e. surgery into a negatively curved space. However, when comes to the non-triangulable case, the surgery process doesn’t work, because the examples of non-triangulable manifolds are topologically constructed by “waving hands”; it’s hard to follow the geometric structure when tring to hyperbolize the non-triangulable manifolds.

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我是E_8 manifold，知乎用户笑颜之花。目前是一名数学专业的本科生，学习兴趣是偏拓扑一些的几何，曾经读过三角剖分猜想、庞加莱猜想等topic。大致上学习了同调论、微分流形、黎曼几何的知识，参加了2025年的几何与拓扑丘赛，取得了个人优胜奖。

我的一句座右铭是“当好自己终生的通识教育导师”，于是我涉猎广泛，如 口琴，伤口包扎，电脑维修，游泳，裁缝，理发等等，但做的不精；现在正准备练习钢琴，将来会考虑学习电气电路的知识，并做一些电子小手工。我现在很羡慕一些建模师的作品，3D动画能够实现一些几何变换的可视化，比如B站用户璐十二的作品。我很希望我也能掌握这种技能，能帮我获得更健全的几何直观。

关于影视作品的爱好，我上小学和初中时看的动画比较多，其中传播真善美的部分也部分地塑造了我的价值观。我喜欢一些洋溢青春活力的作品，比如《比宇宙更远的地方》，讲的是4名中学生克服种种困难，坐上南极科考船去南极的故事；再比如《穿越时空的少女》，女主角是一个比较“跳脱”的高中生绀野真琴(就是我主页的头像)，和两名男生的朋友关系很好，在她意外获得“time leap”的能力之后，不出所料地发生了一些有趣的故事，有情感，有尴尬，有逃避，皆是青春的五味杂陈。

我的主页采用了一套成熟的模板Academic Pages template，在 Publications，CV等模块还留了一些模板的内容没有删除。