Anne Larsen

activity

20192026

collaborators

8 papers

math.AG2026

Fourier duality on compactified Prym fibrations

Anne Larsen

We study Fourier-Mukai duality for a class of compactified Prym fibrations including moduli spaces of $SL$ Higgs bundles over the elliptic locus. This leads to a shadow of…

math.AG2026

Mapping class group action on the cohomology of the $SL_{n}$ character variety

Anne Larsen

We describe the mapping class group action on the cohomology of the twisted $SL_{n}$ -character variety of a surface $Σ_{g}$ of genus $g$ . Our main tool is a relative version o…

math.AG2024

Reider-type theorems on normal surfaces via Bridgeland stability

Anne Larsen, Anda Tenie

Using Langer's construction of Bridgeland stability conditions on normal surfaces, we prove Reider-type theorems generalizing the work done by Arcara-Bertram in the smooth case. Ou…

math.NT2021

Some Remarks on Small Values of $τ (n)$

Kaya Lakein, Anne Larsen

A natural variant of Lehmer's conjecture that the Ramanujan $τ$ -function never vanishes asks whether, for any given integer $α$ , there exist any $n \in Z^{+}$ such that $τ(n…

math.NT2021

A Proof of Merca's Conjectures on Sums of Odd Divisor Functions

Kaya Lakein, Anne Larsen

In a recent paper, Merca posed three conjectures on congruences for specific convolutions of a sum of odd divisor functions with a generating function for generalized $m$ -gonal num…

math.NT2021

Supersingular Loci from Traces of Hecke Operators

Kevin Gomez, Kaya Lakein, Anne Larsen

A classical observation of Deligne shows that, for any prime $p \geq 5$ , the divisor polynomial of the Eisenstein series $E_{p - 1} (z)$ mod $p$ is closely related to the supersingula…

math.DS2020

Strongly Obtuse Rational Lattice Triangles

Anne Larsen, Chaya Norton, Bradley Zykoski

We classify rational triangles which unfold to Veech surfaces when the largest angle is at least $\frac{3 π}{4}$ . When the largest angle is greater than $\frac{2 π}{3}$ , we show that…

math.NT2019

Multiplicative Series, Modular Forms, and Mandelbrot Polynomials

Michael Larsen

We say a power series $\sum_{n = 0}^{\infty} a_{n} q^{n}$ is multiplicative if the function $n \mapsto a_{n} / a_{1}$ ( $n \geq 1$ ) is so. In this paper, we consider multiplicative power series $f$ …

Fourier duality on compactified Prym fibrations

Mapping class group action on the cohomology of the SLn​ character variety

Reider-type theorems on normal surfaces via Bridgeland stability

Some Remarks on Small Values of τ(n)

A Proof of Merca's Conjectures on Sums of Odd Divisor Functions

Supersingular Loci from Traces of Hecke Operators

Strongly Obtuse Rational Lattice Triangles

Multiplicative Series, Modular Forms, and Mandelbrot Polynomials

Mapping class group action on the cohomology of the $SL_{n}$ character variety

Some Remarks on Small Values of $τ (n)$