2 citations · 4 across the 13 of their papers we have counts for
13 papers
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 $…
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.…
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…
Matrix Calculus (for Machine Learning and Beyond)
Paige Bright, Alan Edelman, Steven G. Johnson
This course, intended for undergraduates familiar with elementary calculus and linear algebra, introduces the extension of differential calculus to functions on more general vector…
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 and , we study sets of the for…
Spread Furstenberg Sets
Paige Bright, Manik Dhar
We obtain new bounds for (a variant of) the Furstenberg set problem for high dimensional flats over . In particular, let , ,…
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 Borel and be a…
Radial Projections in Revisited
Paige Bright, Yuqiu Fu, Kevin Ren
We generalize the recent results on radial projections by Orponen, Shmerkin, Wang using two different methods. In particular, we show that given Borel set…
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…
On a radial projection conjecture and pinned directions in finite spaces
Paige Bright, Ben Lund, Thang Pham
We give upper bounds on the number of exceptional radial projections of arbitrary subsets of vector spaces over finite fields. Our bounds do not depend on the dimension of the ambi…
Generalized point configurations in
Paige Bright, Xinyu Fang, Barrett Heritage +4
In this paper, we generalize \cite{IosevichParshall}, \cite{LongPaths} and \cite{cycles} by allowing the \emph{distance} between two points in a finite field vector space to be def…
Improved bounds for embedding certain configurations in subsets of vector spaces over finite fields
Paige Bright, Xinyu Fang, Barrett Heritage +2
The fourth listed author and Hans Parshall (\cite{IosevichParshall}) proved that if , , and is a connected graph on vertices such that…
Exceptional set estimates in finite fields
Paige Bright, Shengwen Gan
We study the exceptional set estimate for projections in . For each , let be the projection map. We…