Presentations

Invited Talks

Positive proportions of elliptic curves with small $2$-Selmer rank
Positive proportions of elliptic curves with small $2$-Selmer rank, Part II
Second moments for $2$-Selmer structures on elliptic curves, and applications
Second moments for $2$-Selmer groups and $2$-class groups
Second moments for $2$-class groups in families of cubic fields
  • Conference on Statistics of Class Groups and Number Fields, ETH Zürich, 2025
Toward secondary terms for 2-Selmer groups in families of elliptic curves
A positive proportion of hyperelliptic curves have no unexpected quadratic points
Geometry-of-numbers in the cusp, and class groups of orders in number fields
Affine symmetric spaces and class groups of cubic fields
The second moment of the size of the 2-Selmer group of elliptic curves
  • Special Session on Arithmetic Statistics, JMM 2023, 2023
Geometry-of-numbers methods in the cusp, and class groups of orders in number fields
  • Number Theory Seminar, MIT, 2022
2-Selmer groups, 2-class groups, and the arithmetic of binary forms
On the distribution of 2-Selmer groups of hyperelliptic Jacobians
  • Workshop on Rational Points on Higher-Dimensional Varieties, ICMS Edinburgh, 2022
Geometry-of-numbers methods in the cusp, and applications to class groups
  • Montreal Online Biweekly Inter-University Seminar on Analytic Number Theory (MOBIUS ANT), 2022
The second moment of the size of the $2$-Selmer group of elliptic curves
$2$-Selmer groups, $2$-class groups, and the arithmetic of binary forms
Average $2$-torsion in the class groups of rings associated to binary $n$-ic forms
Most hyperelliptic curves are pointless
Inflectionary invariants for plane curve singularities
  • Special Session on Research in Mathematics by Undergraduates, JMM 2018, 2018
Surjectivity of Galois representations in rational families of abelian varieties
Inflection points of linear systems on families of curves
Analysis on surreal numbers: functions and integration
Surreal analysis: an analogue of real analysis for surreal numbers

Contributed Talks

Poitou-Tate duality, the 2-Selmer hypercube-graph correspondence, and the Poonen-Rains heuristics
Finite moments for $\mathbb{Q}(i)$-ranks for elliptic curves over $\mathbb{Q}$
  • Lightning Talk at Workshop on Algebraic Points on Curves, ICERM, 2024
Toward secondary terms for 2-Selmer groups in families of elliptic curves
A positive proportion of monic odd hyperelliptic curves have no unexpected quadratic points
Most odd-degree binary forms fail to primitively represent a square
  • Lightning Talk at Annual Meeting of Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation, 2022
Counting lattice points in cusps of fundamental domains
Three lectures on the average size of $2$-Selmer groups of elliptic curves
On the paucity of soluble superelliptic equations
Inflectionary invariants for local complete intersection curve singularities
Inflectionary invariants for plane curve singularities
Surjectivity of Galois representations in rational families of abelian varieties
Permutations that destroy arithmetic progressions in elementary $p$-groups
Elliptic curve variants of the least quadratic nonresidue problem and Linnik's Theorem
Permutations that destroy arithmetic progressions
On arboreal Galois representations of rational functions
How small is that prime?
Arboreal Galois representations of rational functions
Surreal analysis: an analogue of real analysis for surreal numbers
  • Harvard Math Table, 2013
  • CMS Summer Meeting, 2013