Lvzhou(Joe) Chen's Home Page


I am currently a fourth-year graduate student in the Department of Mathematics at the University of Chicago.

I am interested in geometric topology and geometric group theory. Currently, I am working on stable commutator length.

My advisor is Prof. Danny Calegari.

Here is my CV.

As for my names, Lvzhou Chen and Lyuzhou Chen come from Pinyin of my Chinese name 陈绿洲. Unfortunately, the pronunciation of my Chinese name usually does not make much sense to English speakers. If this is the case for you, just call me Joe.

Thanks for the guide produced by Zev Chonoles, which is great for beginners to set up their home pages. I would be glad to get any suggestions for improving my homepage.


Photo by Le Zhuang


Spectral gap of scl in free products, Proc. Amer. Math. Soc. 146 (2018), no.7, 3143-3151
Abstract: We show that for a free product G of torsion-free groups, scl(g) is at least 1/2 for any g in [G,G] not conjugate into any factor. This generalizes, and gives a new proof of a theorem of Duncan-Howie.

Scl in free products, Algebr. Geom. Topol., to appear. arXiv: 1611.07463
Abstract: We show that scl is rational in free products of groups with vanishing scl, generalizing a theorem of Danny Calegari. We further prove that the property of isometric embedding with respect to scl is preserved under taking free products. The method of proof gives a way to compute scl in free products which lets us generalize and derive in a new way several well-known formulas. Finally we show independently and in a new approach that scl in free products of cyclic groups behaves in a piecewise quasi-rational way when the word is fixed but the orders of factors vary, previously proved by Timothy Susse, settling a conjecture of Alden Walker.


Topic Proposal: Stable Commutator Length


Spectral gap of scl, 2017 Fall AMS sectional meeting at Buffalo


Email: lzchen (followed by
Mail: Department of Mathematics
University of Chicago
5734 S. University Avenue
Chicago, IL, 60637
Office: Eckhart 105


Research Blog of Prof. Danny Calegari
Low Dimensional Topology Blog