William Slofstra

William Slofstra is an Associate Professor in the Department of Pure Mathematics at the University of Waterloo and a member of the Institute for Quantum Computing. His primary academic home is within the Faculty of Mathematics at Waterloo, where he contributes to both pure mathematical research and quantum information science.

Slofstra's research spans two major areas: the mathematics of quantum information and computation, and classical areas of Lie theory and algebraic combinatorics. Within quantum information, his main interests include non-local games, quantum correlation sets, self-testing and device-independence, entanglement theory, and multi-prover interactive proofs. He also investigates new mathematical tools such as decision problems in operator algebras and approximate representation theory that could advance these areas. In Lie theory and algebraic combinatorics, his research focuses on Kac-Moody groups and algebras, Schubert varieties, Coxeter groups, and hyperplane arrangements.

His publication record shows a strong trajectory from more classical mathematical research toward quantum information theory, with recent work demonstrating deep connections between group theory and quantum non-locality. His most significant contributions include proving that the set of quantum correlations is not closed, establishing undecidability results for quantum correlation membership problems, and developing connections between hyperlinear profiles of groups and entanglement requirements in non-local games.

Slofstra maintains an active research program with numerous collaborations, particularly with Ed Richmond in the area of Schubert varieties and with various researchers in quantum information. His work has appeared in top journals including the Journal of the American Mathematical Society, Forum of Mathematics Pi, and the Computational Complexity Conference.

He is engaged in educational activities, having worked on turning his notes for PMATH 343 into a book titled 'Linear algebra and quantum probability.' He also maintains a podcast and YouTube channel, though he notes he has minimal social media presence.