Raymond Cheng
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.
Writings
Here is a collection of writings, at various stages of completion, that I have done over the years.Research
 Higher Cycle Operations and a Unipotent Torelli Theorem for Graphs (with Eric Katz).
 Combinatorial aspects of the quantized universal enveloping algebra of \(\mathfrak{sl}_{n+1}(\mathbf{C})\) (with David M. Jackson and Geoff Stanley).
Expository

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.

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.
Teaching
 Fall 2018 — Undergraduate seminar on Combinatorial Reciprocity Theorems.
 Summer 2018 — TA for REU on Curves on Surfaces Over Finite Fields, led by Daniel Litt and Alex Perry.
 Spring 2018 — TA for Schemes taught by Johan de Jong.
 Spring 2018 — TA for Honours Mathematics B taught by David Hansen.
 Fall 2017 — Undergraduate seminar on Hodge Theory in Combinatorics.
 Fall 2017 — TA for Commutative Algebra, taught by Johan de Jong.
 Summer 2017 — TA for REU on Representation Theory in Graph Theory, led by David Hansen and Daniel Litt.
Seminars
 Fall 2018 — Cubic Fourfolds, Rationality, etc.
 Summer 2018 — (with Shizhang Li) Integral \(p\)adic Hodge theory.
 Spring 2018 — Topics on Abelian Varieties.
 Fall 2017 — (with Carl Lian) Moduli of Sheaves.
 Summer 2017 — (with Carl Lian) Classic Papers in Algebraic Geometry.