2 papers
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
Tangency counting for well-spaced circles
Dominique Maldague, Alexander Ortiz
In the late 90's, Tom Wolff introduced the circle tangency counting problem in his expository article on the Kakeya conjecture. For collections of well-spaced circles, we break the…