Carl Lian


I am a fourth-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 geometry. Recently, I've been thinking about moduli of curves, Brill-Noether theory, and related enumerative questions, as well as Alexander-Hirschowitz/SHGH-type interpolation problems.

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


  • Enumerating pencils with moving ramification on curves, in preparation.
  • The Class of the d-elliptic Locus in Genus 2, preliminary draft as of September 2017. Poster, Talk, Talk Notes. (I expect to revise this paper in the near future.)
  • (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.


  • Summer 2019: Instructor for Calculus 1
  • Spring 2019: TA for Algebraic Geometry (Instructor: Johan de Jong)
  • Fall 2018: Instructor for Calculus 1
  • Summer 2018: TA for Calculus 1 (Instructor: Shuai Wang)
  • 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