New bounds on curve tangencies and orthogonalities

Joshua Zahl, MIT

January 26, 2016

In the past several years, progress has been made on several questions in combinatorial geometry by first embedding the problem into a higher dimensional space. In this talk, I will discuss some new bounds on the number of tangencies and orthogonal intersections determined by an arrangement of plane curves. The main innovation is a new method that transforms arrangements of plane curves into arrangements of space curves.

This is joint work with Jozsef Solymosi.