Speaker: Aryaman Jal.

Affiliation:  KTH, Stockholm.

Time: 5-6pm, Thursday, 6 July.

Venue:  Room 216, Mathematics Department.

Host : Madhusudan Manjunath

Title: Polyhedral geometry of bisectors and bisection fans.


Abstract: Every symmetric convex body induces a norm on its affine hull.
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 (2021)
expanded this to a deeper study 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. We 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.