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.