Department of Mathematical Sciences
QIT Thinking Seminar
Wednesday, September 10th, 2025
Stratton Hall 207, 4:00PM- 4:50 PM
Speaker: Bill Martin, WPI
Title: Quantum permutation matrices
Abstract: In joint work with Ada Chan on the quantum isomorphism game, I got interested in quantum permutation matrices. These give winning strategies for various quantum games but also serve as an entry point to the more abstract basic theory of compact matrix quantum groups. The main goal of the talk is to give examples, involving both commutative and non-commutative C*-algebras, but I also hope to touch upon the fundamental examples of compact matrix quantum groups. If A is a C*-algebra and P is a matrix with entries p_ij in A, we call P a quantum permutation matrix if all rows and columns sum to the identity element of A and each entry of P satisfies p_ij = p_ij* = p_ij^2 . Our preferred examples are where these entries are matrices, but we want to avoid the trivial case where they commute.