Yuhang Liu

Yuhang Liu

About me

I have graduated and moved to BICMR to be a postdoc there. Please contact me at 532258137@qq.com or liuyuhang.fudan@gmail.com.

I am a recent PhD in mathematics at the University of Pennsylvania. I am interested in differential geometry and geometric analysis. My advisor is Wolfgang Ziller.

Before joining Penn I had a B.Sc in Mathematics and from Fudan University, Shanghai, China.

Research Interest

I am interested in Riemannian manifolds of positive sectional curvature. Currently I am studying the topology of
6-dimensional Riemannian manifolds with positive sectional curvature invariant under certain isometric actions by SU(2) or SO(3). I obtained several results in this direction, including the Euler characteristic bound and diffeomorphism classification when the action has no exceptional orbits.

I am also interested in problems related to Sasaki-Einstein metrics and homogeneous Einstein metrics.

Curriculum Vitae

You can find a copy of my CV here.

Contact information

Office : Room 4C5, DRL
E-mail : yuhliu[AT]math[DOT]upenn[DOT]edu

Notes and Surveys

  1. PhD thesis
  2. Research Statement
  3. On the structure of orbit spaces of certain SU(2) or SO(3) actions on positively curved 6-manifolds Notes on Examples
  4. Useful survey paper from my advisor, if you want to have a basic idea of positively curved geometry Riemannian manifolds with positive sectional curvature
  5. Grove's paper on symmetry program geometry of and via symmetries


I like playing table tennis and Go. I'm amateur 1 dan in Go. On AGA website you can find lots of resources on learning Go. Or you can come to my office and let me teach.
For people who know how to play Go, AlphaGo Teach is a great place to improve skills.
I also like to play board games, including but not limited to Avalon.
I am also a user of Zhihu, which is a Chinese website for asking and answering questions, like Quora.
I am a beginning user of MathOverFlow.


Fall 2018: Math 618, Algebraic topology
Homework Solutions:
HW 1 HW 2 HW 3
Summer Session I 2017 : Math 114, Calculus II (Instructor)
Fall 2016 : Math 104, Calculus I (Teaching Assistant)
Spring 2016 : Math 312, Linear Algebra (Grader)