Aaron Landesman

activity

20142025

most citedSurjectivity of Galois Representations in Rational Families of Abelian Varieties

16 citations · 61 across the 27 of their papers we have counts for

collaborators

34 papers

math.AG2025

The locus of plane curves in the moduli stack of curves

Aaron Landesman

Let $d \geq 4$ and let $U_{d}$ denote the locus of smooth curves in the Hilbert scheme of degree $d$ plane curves. If the members of $U_{d}$ have genus $g$ , let $M_{g}$ denote…

math.AG2024

Big monodromy for higher Prym representations

Aaron Landesman, Daniel Litt, Will Sawin

Let $Σ_{g^{'}} \to Σ_{g}$ be a cover of an orientable surface of genus g by an orientable surface of genus g', branched at n points, with Galois group H. Such a cover induces a virtual a…

math.NT2023

Homological stability for generalized Hurwitz spaces and Selmer groups in quadratic twist families over function fields

Jordan S. Ellenberg, Aaron Landesman

We prove a version of the Bhargava-Kane-Lenstra-Poonen-Rains heuristics for Selmer groups of quadratic twist families of abelian varieties over global function fields. As a consequ…

math.AG2023

Finite braid group orbits on $S L_{2}$ -character varieties

Yeuk Hay Joshua Lam, Aaron Landesman, Daniel Litt

Let X be a 2-sphere with n punctures. We classify all conjugacy classes of Zariski-dense representations $ρ : π_{1} (X) \to S L_{2} (C)$ with finite orbit under the mapping class…

math.AG2023

Obstructions to applying the Baker--Bilu method for determining integral points on curves

Aaron Landesman, Bjorn Poonen

We prove that for every smooth projective integral curve $X$ of genus at least $2$ over $C$ , there exists $x \in X (C)$ such that no connected finite étale cover of…

math.AG2022

Prill's problem

Aaron Landesman, Daniel Litt

We solve Prill's problem, originally posed by David Prill in the late 1970s and popularized in ACGH's "Geometry of Algebraic Curves." That is, for any curve $Y$ of genus $2$ , we pr…

math.AG2022

Applications of the algebraic geometry of the Putman-Wieland conjecture

Aaron Landesman, Daniel Litt

We give two applications of our prior work toward the Putman-Wieland conjecture. First, we deduce a strengthening of a result of Marković-Tošić on virtual mapping class group actio…

math.AG2022★ 2 cited

An introduction to the algebraic geometry of the Putman-Wieland conjecture

Aaron Landesman, Daniel Litt

We give algebraic and geometric perspectives on our prior results toward the Putman-Wieland conjecture. This leads to interesting new constructions of families of "origami" curves…

math.GT2022★ 2 cited

Canonical representations of surface groups

Aaron Landesman, Daniel Litt

Let $Σ_{g, n}$ be an orientable surface of genus $g$ with $n$ punctures. We study actions of the mapping class group of $Σ_{g, n}$ via Hodge-theoretic and arithmetic techniques. We s…

math.AG2022★ 2 cited

Low degree Hurwitz stacks in the Grothendieck ring

Aaron Landesman, Ravi Vakil, Melanie Matchett Wood

For $2 \leq d \leq 5$ , we show that the class of the Hurwitz space of smooth degree $d$ , genus $g$ covers of $P^{1}$ stabilizes in the Grothendieck ring of stacks as $g \to \…

math.AG2022★ 1 cited

Geometric local systems on very general curves and isomonodromy

Aaron Landesman, Daniel Litt

We show that the minimum rank of a non-isotrivial local system of geometric origin, on a suitably general $n$ -pointed curve of genus $g$ , is at least $2 g + 1$ . We apply this r…

math.NT2021

Stacky heights on elliptic curves in characteristic 3

Aaron Landesman

We show there are no stacky heights on the moduli stack of stable elliptic curves in characteristic $3$ which induce the usual Faltings height, negatively answering a question of E…

math.NT2021

A geometric approach to the Cohen-Lenstra heuristics

Aaron Landesman

We give a new geometric description of when an element of the class group of a quadratic field, thought of as a quadratic form $q$ , is $n$ -torsion. We show that $q$ corresponds to…

math.AG2020

A Fulton-Hansen theorem for almost homogeneous spaces

János Kollár, Aaron Landesman

We prove a generalization of the Fulton-Hansen connectedness theorem, where $P^{n}$ is replaced by a normal variety on which an algebraic group acts with a dense orbit.

math.AG2020

A Lefschetz theorem for intersections with projective varieties

Aaron Landesman

One version of the classical Lefschetz hyperplane theorem states that for $U \subset P^{n}$ a smooth quasi-projective variety of dimension at least $2$ , and $H \cap U$ a gene…

math.AG2020

Invariance of the tame fundamental group under base change between algebraically closed fields

Aaron Landesman

We show that the tame étale fundamental group of a connected normal finite type separated scheme remains invariant upon base change between algebraically closed fields of character…

math.NT2020★ 1 cited

The geometric distribution of Selmer groups of elliptic curves over function fields

Tony Feng, Aaron Landesman, Eric M. Rains

Fix a positive integer $n$ and a finite field $F_{q}$ . We study the joint distribution of the rank of $E$ , the $n$ -Selmer group of $E$ , and the $n$ -torsion in the Tate-Shafar…

math.AG2019★ 2 cited

The infinitesimal Torelli problem

Aaron Landesman

Let $g \geq 2$ and let the Torelli map denote the map sending a genus $g$ curve to its principally polarized Jacobian. We verify the well known fact that the map induced on tangent…

math.AG2019

The Torelli map restricted to the hyperelliptic locus

Aaron Landesman

Let $g \geq 2$ and let the Torelli map denote the map sending a genus $g$ curve to its principally polarized Jacobian. We show that the restriction of the Torelli map to the hypere…

math.NT2019★ 6 cited

Improved lower bounds for the number of fields with alternating Galois group

Aaron Landesman, Robert J. Lemke Oliver, Frank Thorne

Let $n \geq 6$ be an integer. We prove that the number of number fields with Galois group $A_{n}$ and absolute discriminant at most $X$ is asymptotically at least $X^{1/8 + O (1/ n)}$ .…

math.NT2018★ 9 cited

The geometric average size of Selmer groups over function fields

Aaron Landesman

We show, in the large $q$ limit, that the average size of $n$ -Selmer groups of elliptic curves of bounded height over $F_{q} (t)$ is the sum of the divisors of $n$ . As a corol…

math.NT2018

An explicit Abelian surface with maximal Galois action

Quinn Greicius, Aaron Landesman

We construct an explicit example of a genus $2$ curve $C$ over a number field $K$ such that the adelic Galois representation arising from the action of $\operatorname{Gal}(\overlin…

math.NT2017★ 6 cited

Hyperelliptic Curves with Maximal Galois Action on the Torsion Points of their Jacobians

Aaron Landesman, Ashvin Swaminathan, James Tao +1

In this article, we show that in each of four standard families of hyperelliptic curves, there is a density- $1$ subset of members with the property that their Jacobians have adelic…

math.NT2016★ 2 cited

The twisting Sato-Tate group of the curve $y^{2} = x^{8} - 14 x^{4} + 1$

Sonny Arora, Victoria Cantoral-Farfán, Aaron Landesman +2

We determine the twisting Sato-Tate group of the genus $3$ hyperelliptic curve $y^{2} = x^{8} - 14 x^{4} + 1$ and show that all possible subgroups of the twisting Sato-Tate group arise…

The locus of plane curves in the moduli stack of curves

Big monodromy for higher Prym representations

Homological stability for generalized Hurwitz spaces and Selmer groups in quadratic twist families over function fields

Finite braid group orbits on SL2​-character varieties

Obstructions to applying the Baker--Bilu method for determining integral points on curves

Prill's problem

Applications of the algebraic geometry of the Putman-Wieland conjecture

An introduction to the algebraic geometry of the Putman-Wieland conjecture

Canonical representations of surface groups

Low degree Hurwitz stacks in the Grothendieck ring

Geometric local systems on very general curves and isomonodromy

Stacky heights on elliptic curves in characteristic 3

A geometric approach to the Cohen-Lenstra heuristics

A Fulton-Hansen theorem for almost homogeneous spaces

A Lefschetz theorem for intersections with projective varieties

Invariance of the tame fundamental group under base change between algebraically closed fields

The geometric distribution of Selmer groups of elliptic curves over function fields

The infinitesimal Torelli problem

The Torelli map restricted to the hyperelliptic locus

Improved lower bounds for the number of fields with alternating Galois group

The geometric average size of Selmer groups over function fields

An explicit Abelian surface with maximal Galois action

Hyperelliptic Curves with Maximal Galois Action on the Torsion Points of their Jacobians

The twisting Sato-Tate group of the curve y2=x8−14x4+1

Finite braid group orbits on $S L_{2}$ -character varieties

The twisting Sato-Tate group of the curve $y^{2} = x^{8} - 14 x^{4} + 1$