__Carl Lian__

I am a fifth-year graduate student in mathematics at Columbia University, advised by Aise Johan de Jong. I was previously supported by an NSF Graduate Research Fellowship. Before that, I graduated from MIT in June 2015 with an S.B. in mathematics and minor in music.

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

**Current news (Fall 2019)**

I am currently on the academic job market. To this end, here is my CV.
I am travelling a fair bit this semester; here is my itinerary.
I am the TA for Johan de Jong's Commutative Algebra course this semester. My help room hours are TBD.
**Research**

I'm broadly interested in algebraic geometry. Some specific things I like thinking about are:

Intersection theory on moduli spaces of curves and branched covers, including combinatorial aspects
Brill-Noether theory, limit linear series, and related enumerative problems
Syzygies of curves
Interpolation of curves in higher-dimensional varieties
Linear systems of singular divisors, e.g. the SHGH conjecture and related problems
Here are my papers:

Enumerating pencils with moving ramification on curves, arXiv 1907.09087.
The class of the d-elliptic Locus in genus 2, arXiv 1907.08991. Here is a video of my talk at ICTP on this work.
(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.
**Old Links** (past teaching, seminars organized, etc.)