Abstract for the talk on 07.12.2017 (14:00 h)

Seminar on Nonlinear Algebra

Kristin Shaw (MPI MIS, Leipzig)
Designs as tropical varieties

A T-design is a collection of subsets of a set X of size k, called "blocks", such that every subset of X of size T is contained in lambda blocks. Examples of designs are magic and latin squares, Hadamard matrices, Steiner systems, finite projective planes, to name just a few.

 

From a T-design I will show how to construct a T-dimensional tropical variety of degree lambda. Then using this construction, I will interpret some operations on designs through an algebro-geometric lens. This work is very much in progress and comments/suggestions are welcome.

 

09.12.2017, 02:20