Ben Williams

Ben Williams is an Associate Professor in the Department of Mathematics at the University of British Columbia, Faculty of Science. His office is located in MATX 1205 in UBC's Math Annex building. He is actively involved in research supervision, teaching undergraduate courses including Math 221 (Matrix Algebra) and Math 426 (Introduction to Topology), and has developed educational resources such as a free online textbook for Math 221.

Dr. Williams' research focuses on algebraic topology, motivic homotopy theory, and A1 homotopy theory, with particular emphasis on applying homotopy-theoretic methods to problems in algebra and algebraic geometry. His work has significantly advanced understanding of Azumaya algebras, Brauer groups, and the period-index problem. His research bridges abstract algebra with topological methods, creating novel connections between seemingly disparate mathematical domains. He has made substantial contributions to the understanding of the relationship between period and index of Brauer classes, extending classical results using modern homotopy-theoretic techniques.

Analysis of Dr. Williams' publication record reveals a consistent trajectory of sophisticated work at the intersection of algebra and topology. His collaborations with mathematicians like Ben Antieau, Aravind Asok, and Uriya First demonstrate his position within an active research network. His publications in top journals including Inventiones Mathematicae, Geometry & Topology, and Journal of the European Mathematical Society reflect the high impact of his research. The progression of his work shows increasing depth in applying motivic homotopy theory to solve challenging problems in algebraic geometry and representation theory.

Dr. Williams is actively involved in mentoring the next generation of mathematicians, currently supervising PhD student Sebastian Gant and MSc students Molly Blackburn and Peilin Li. He has organized several major conferences including multiple Cascade Topology Seminars, the New Trends in Algebra, Geometry and Homotopy Theory conference, and the Séminaire de Mathématiques Supérieures 2022 on Floer Homotopy Theory. His service to the mathematical community through conference organization and editorial work demonstrates his commitment to advancing research in his field and fostering academic collaboration.