7 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 $…
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…
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…
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 , ,…
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…