Carl Lian


I am a third-year graduate student in mathematics at Columbia University, advised by Aise Johan de Jong and currently supported by an NSF Graduate Research Fellowship. I graduated from MIT in June 2015 with an S.B. in Mathematics and minor in Music.

I'm interested broadly in algebraic and arithmetic geometry. Recently I've been thinking about moduli of curves, Brill-Noether theory, and related enumerative questions.

Outside of math, I've been involved with the Columbia New Opera Workshop since Spring 2017.


  • The Class of the d-elliptic Locus in Genus 2, preliminary draft.
  • (with Joshua Alman and Brandon Tran) Circular Planar Electrical Networks: Posets and Positivity. J. Combinatorial Theory, Ser. A 132, 58-101 (2015).
  • Representations of Cherednik Algebras Associated to Symmetric and Dihedral Groups in Positive Characteristic, arXiv 1207.0182.


  • Fall 2017: TA for Calculus 1 (Instructor: Dusa McDuff)
  • Fall 2016: TA for Calculus 1 (Instructor: Dusa McDuff)

    Seminar organizing:

  • Fall 2017 (with Raymond Cheng): Moduli of Sheaves
  • Summer 2017 (with Raymond Cheng): Classic Papers in Algebraic Geometry
  • Spring 2017 (with Shizhang Li): BBD
  • Fall 2016 (with Shizhang Li): Hodge Theory in Positive Characteristic

    Mostly old activities:

  • Columbia Mathematics REU
  • Harvard-MIT Mathematics Tournament
  • Combinatorics REU, U. Minnesota-Twin Cities
  • Lexington Mathematics Tournament and Lexington High School's math club.
  • Canada/USA Mathcamp