Caleb Marshall

activity

20242026

collaborators

8 papers

math.CA2026

Nearly Sharp Uniform Projection Bounds and Superlinear Vitushkin Inequalities for Deterministic Self-Similar Sets

Caleb Marshall

For each $α \in (0, 1)$ , we construct an explicit deterministic finite homogeneous planar iterated function system of similarities satisfying the strong separation condition, whose at…

math.CA2026

Finite Good Witnesses for Generalized Curve Projections at the Rectifiable Endpoint

Caleb Marshall

For a $1$ -rectifiable set $E \subset R^{d}$ of positive length, a theorem of Federer shows that, among any $d$ linearly independent orthogonal projections of $E$ , at least o…

math.CA2026

Applications of Nonlinear Projections to Rectifiable 1-sets

Rosemarie Bongers, Paige Bright, Caleb Marshall +1

Projection theorems in Euclidean space provide a fundamental link between the geometric structure of a set and the size of its lower-dimensional images. For 1-rectifiable sets in $…

math.CA2025

Improved Power Laws for the Favard Length Problem in All Dimensions

Caleb Marshall

The Favard length of a compact set in $R^{d}$ is the average one-dimensional Hausdorff measure of its orthogonal projections onto lines. We establish quantitative upper boun…

math.NT2025

Lower bounds for mask polynomials with many cyclotomic divisors

Gergely Kiss, Izabella Łaba, Caleb Marshall +1

Given a nonempty set $A \subset N \cup {0}$ , define the mask polynomial $A (X) = \sum_{a \in A} X^{a}$ . Suppose that there are $s_1,\dots,s_k\in\nn\setminus\{1\}$ such that the…

math.CA2024

Pinned Dot Product Set Estimates

Paige Bright, Caleb Marshall, Steven Senger

We study a variant of the Falconer distance problem for dot products. In particular, for fractal subsets $A \subset R^{n}$ and $a, x \in R^{n}$ , we study sets of the for…

math.CA2024

A Continuum Erdős-Beck Theorem

Paige Bright, Caleb Marshall

We prove a version of the Erdős--Beck Theorem from discrete geometry for fractal sets in all dimensions. More precisely, let $X \subset R^{n}$ Borel and $k \in [0, n - 1]$ be a…

math.CA2024

A Study Guide to "Kaufman and Falconer estimates for radial projections"

Paige Bright, Ryan Bushling, Caleb Marshall +1

This expository piece expounds on major themes and clarifies technical details of the paper "Kaufman and Falconer estimates for radial projections and a continuum version of Beck's…