Raymond Cheng

rcheng at math dot columbia dot edu

Department of Mathematics
Columbia University
2990 Broadway
New York, NY 10027

I am a third year mathematics graduate student at Columbia University Sometimes, I heed the advice of Johan de Jong. Geometry fascinates me, with algebraic methods my preferred means of exploration.


Here is a collection of writings, at various stages of completion, that I have done over the years.


  1. Higher Cycle Operations and a Unipotent Torelli Theorem for Graphs (with Eric Katz).
  2. Combinatorial aspects of the quantized universal enveloping algebra of \(\mathfrak{sl}_{n+1}(\mathbf{C})\) (with David M. Jackson and Geoff Stanley).


  1. Projectivity of moduli of curves

    This is a draft of an exposition of Kollár's proof of the projectivity of the moduli space of stable curves. This was started at the Stacks Project Workshop during August of 2017 together with Yordanka Kovacheva, Carl Lian, Monica Marinescu, and Takumi Murayama, with guidance from Davesh Maulik. The source code for this project is available here.

  2. Positivity through broken lines

    This is an expository note on the proof due to Gross–Hacking–Keel–Kontsevich (see this) of the positiviy of the Laurent Phenomenon conjecture for cluster algebras. This was written for a course taught by Lauren Williams at Columbia in the fall of 2016.