Aryaman Jal: Bisectors of polyhedral norms

Abstract: Every symmetric convex body induces a norm on the underlying space. The object of our study is the bisector of two points with respect to this norm. A topological description of bisectors is known in the 2 and 3-dimensional cases and recent work of Criado, Joswig and Santos expanded this to a fuller characterisation of the geometric, combinatorial and topological properties of the bisector. A key object introduced was the bisection fan of a polytope which they were able to explicitly describe in the case of the tropical norm. In this talk, we will discuss the bisector as a polyhedral complex, introduce the notion of bisection cones and describe the bisection fan corresponding to other polyhedral norms. This is joint work with Katharina Jochemko.

This seminar will be given in person.