Paige Bright

activity

20232026

most citedMatrix Calculus (for Machine Learning and Beyond)

2 citations · 2 across the 11 of their papers we have counts for

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8 papers · 1 filter

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

A Continuum Beck-type Theorem for Hyperplanes

Paige Bright, Alexander Ortiz, Dmitrii Zakharov

We prove a sharp continuum Beck-type theorem for hyperplanes. Our work is inspired by foundational work of Beck on the discrete problem, as well as refinements due to Do and Lund.…

math.CA2025

Progress in Projection Theory and other dimensional developments

Paige Bright

We provide exposition into the field of projection theory, which lies at the intersection of incidence geometry and geometric measure theory. We first give the necessary preliminar…

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

Spread Furstenberg Sets

Paige Bright, Manik Dhar

We obtain new bounds for (a variant of) the Furstenberg set problem for high dimensional flats over $R^{n}$ . In particular, let $F \subset R^{n}$ , $1 \leq k \leq n - 1$ ,…

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…