Our Friend the Transpose

This page is for the keynote presentation by Dr. Ben Williams.

Abstract

The transpose is an order-2 operation on square matrices that preserves addition and reverses multiplication. For complex square matrices, the hermitian conjugate has the same properties. I will consider a sequence of increasingly exotic analogues of these operations. These analogues are related to the topological properties of certain spaces: both familiar and novel. I will try to explain all this.