Hannah Larson

I am a Clay Research Fellow for 2022-2027. During the year 2022-2023, I will be a Junior Fellow at the Harvard Society of Fellows. Starting in Fall 2023, I will join the faculty at the University of California, Berkeley as an Assistant Professor.

I received my PhD from Stanford University in June 2022. My thesis, Brill-Noether theory over the Hurwitz space, was advised by Ravi Vakil.

My email address is hlarson at math dot harvard dot edu. Here is my CV.

Papers and Preprints:

• The bielliptic locus in genus 11 [joint with Samir Canning].
• The eleventh cohomology group of Mbar_{g,n} [joint with Samir Canning and Sam Payne].
• On the Chow and cohomology rings of moduli spaces of stable curves [joint with Samir Canning].
• The rational Chow rings of moduli spaces of hyperelliptic curves with marked points [joint with Samir Canning].
• The integral Picard groups of low-degree Hurwitz spaces [joint with Samir Canning].
• Chow rings of low-degree Hurwitz spaces (Crelle) [joint with Samir Canning].
• On an equivalence of divisors on M_{0,n} bar from Gromov-Witten theory and conformal blocks (Transformation Groups) [joint with Linda Chen, Angela Gibney, Lauren Cranton Heller, Elana Kalashnikov, and Weihong Xu].
• The intersection theory of the moduli space of vector bundles on P1 (Canadian Math Bulletin).
• The Chow rings of the moduli spaces of curves of genus 7, 8, and 9 [joint with Samir Canning].
• Tautological classes on on low-degree Hurwitz spaces [joint with Samir Canning].
• Global Brill-Noether theory over the Hurwitz space [joint with Eric Larson and Isabel Vogt].
• Refined Brill-Noether theory for all trigonal curves (European Journal of Mathematics).
• An enriched count of the bitangents to a smooth plane quartic curve (Research in the Mathematical Sciences) [joint with Isabel Vogt].
• A refined Brill-Noether theory over Hurwitz spaces (Inventiones Mathematicae).
• Universal degeneracy classes for vector bundles on P1 bundles (Advances in Mathematics). Code for Example 5.2: Part 1 and Part 2.
• Normal bundles of lines on hypersurfaces (Michigan Math Journal).
• Hyperbolicity of the partition Jensen polynomials (Research in Number Theory) [joint with Ian Wagner].
• Coefficients of McKay-Thompson series and distributions of the moonshine module (Proceedings of the AMS).
• Shifted distinct-part partition identities in arithmetic progressions (Annals of Combinatorics) [joint with Alwise et al].
• Proof of conjecture regarding the level of Rose's generalized sum-of-divisor functions (Research in Number Theory).
• Modular units from quotients of Rogers-Ramanujan type q-series (Proceedings of the AMS).
• Generalized Andrews-Gordon Identities (Research in Number Theory).
• Traces of singular values of Hauptmoduln (International Journal of Number Theory) [joint with Lea Beneish].
• Congruence properties of Taylor coefficients of modular forms (International Journal of Number Theory) [joint with Geoffrey Smith].
• Pseudo-unitary non-self-dual fusion categories of rank 4 (Journal of Algebra).

Upcoming talks:

• Stanford Algebraic Geometry Seminar, May 5, 2023
• Kentucky-Ohio ALgebra Alliance (KOALA), May 9-10, 2023

Presentation videos:

• 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.

Teaching:

• Winter 2020, Stanford Math 51: Linear Algebra and Multivariable Calculus, Graduate Teaching Assistant (Evaluations) (Review Sheet)
• Summer 2017, Emory University Number Theory Research Experience for Undergraduates, Instructor
• Spring 2016, Harvard Math 137: Algebraic Geometry, Undergraduate Course Assistant (Evaluations)
• Spring 2015, Harvard Math 129: Algebraic Number Theory, Undergraduate Course Assistant (Evaluations)