I am fourth year graduate student at Stanford University,
working on algebraic geometry with Ravi Vakil.
My email address is email@example.com.
Here is my CV.
Papers and Preprints:
- The rational Chow rings of M_7, M_8, and M_9, Derived Seminar, Winter 2021
Abstract: The rational Chow ring of the moduli space M_g of curves of genus g is known for g up to 6. In each of these cases, the Chow ring is tautological (generated by certain natural classes known as kappa classes). In recent joint work with Sam Canning, we prove that the rational Chow ring of M_g is tautological for g = 7, 8, 9, thereby determining the Chow rings by work of Faber. In this talk, I give an overview of our approach, with particular focus on the locus of tetragonal curves (special curves admitting a degree 4 map to P^1).
- Brill-Noether theory over the Hurwitz space, Western Algebraic Geometry Symposium (WAGS) Fall 2020
Abstract: Let C be a curve of genus g. A fundamental problem in the theory of algebraic curves is to understand maps of C to projective space of dimension r of degree d. When the curve C is general, the moduli space of such maps is well-understood by the main theorems of Brill--Noether theory. However, in nature, curves C are often encountered already equipped with a map to some projective space, which may force them to be special in moduli. The simplest case is when C is general among curves of fixed gonality. Despite much study over the past three decades, a similarly complete picture has proved elusive in this case. In this talk, I discuss joint work with Eric Larson and Isabel Vogt that completes such a picture, by proving analogs of all of the main theorems of Brill--Noether theory in this setting.
- A refined Brill-Noether theory over Hurwitz spaces, Algebraic Geometry is Online in Zoom Everyone (AGONIZE), Spring 2020
Abstract: The celebrated Brill-Noether theorem says that the space of degree d maps of a general genus g curve to P^r is irreducible. However, for special curves, this need not be the case. Indeed, for general k-gonal curves (degree k covers of P^1), this space of maps can have many components, of different dimensions (Coppens-Martens, Pflueger, Jensen-Ranganathan). In this talk, I introduce a natural refinement of Brill-Noether loci for curves with a distinguished map C --> P^1, using the splitting type of push forwards of line bundles to P^1. In particular, studying this refinement determines the dimensions of all irreducible components of Brill-Noether loci of general k-gonal curves.