__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.

**Research:**

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.
**Teaching:**

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