11 papers
The coherent KLR sheaf
Matthew Hase-Liu, Fan Zhou
We construct the KLR algebra (in type ) as affine sections of a coherent sheaf on a product of projective spaces . It was shown by Elias-Qi that the…
The asymptotic in Waring's problem over function fields beyond twice the degree
Matthew Hase-Liu
We prove the expected asymptotic in Waring's problem over , with a power-saving error, whenever , the characteristic is greater than , and satisf…
Birch's theorem over function fields with quadratically many variables
Matthew Hase-Liu
For smooth hypersurfaces over rational function fields of characteristic greater than the degree and with sufficiently large constant field, we improve the number of variables requ…
Betti bounds for spaces of curves on varieties and Manin's conjecture for quartic del Pezzo surfaces
Enhao Feng, Matthew Hase-Liu
We prove uniform exponential bounds for the compactly supported Betti numbers of spaces of morphisms from curves of fixed genus to projective varieties. For targets in a fixed proj…
A converse to geometric Manin's conjecture for general low degree hypersurfaces and Poincaré duality
Matthew Hase-Liu
Geometric Manin's conjecture predicts that components of the moduli space of curves on a Fano variety parametrizing non-free curves are pathological and arise from "accumulating" m…
Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method
Jakob Glas, Matthew Hase-Liu
We study the singularities of the moduli space of degree maps from smooth genus curves to an arbitrary smooth hypersurface of low degree. For large compared to , we…
Non-smoothness of Moduli Spaces of Higher Genus Curves on Low Degree Hypersurfaces
Matthew Hase-Liu, Amal Mattoo
We show that the moduli space of degree maps from smooth genus curves to an arbitrary low degree smooth hypersurface is singular when is large compared to . We…
A geometric approach to functional equations for general multiple Dirichlet series over function fields
Matthew Hase-Liu
Sawin recently gave an axiomatic characterization of multiple Dirichlet series over the function field and proved their existence by exhibiting the coefficients…
A higher genus circle method and an application to geometric Manin's conjecture
Matthew Hase-Liu
Browning and Vishe used the Hardy-Littlewood circle method to show the moduli space of rational curves on smooth hypersurfaces of low degree is irreducible and of the expected dime…
Sum-Product Phenomena for Planar Hypercomplex Numbers
Matthew Hase-Liu, Adam Sheffer
We study the sum-product problem for the planar hypercomplex numbers: the dual numbers and double numbers. These number systems are similar to the complex numbers, but it turns out…
Efficient Point-Counting Algorithms for Superelliptic Curves
Matthew Hase-Liu, Nicholas Triantafillou
In this paper, we present efficient algorithms for computing the number of points and the order of the Jacobian group of a superelliptic curve over finite fields of prime order p.…