Rate My Professor Richard Garner

Associate Professor Richard Garner is based in the School of Mathematical and Physical Sciences within the Faculty of Science and Engineering at Macquarie University. He holds an undergraduate MA and a PhD in Mathematics from the University of Cambridge. Following his PhD, Garner held postdoctoral fellowships in the United Kingdom, Sweden, and Australia before taking up his current position at Macquarie University.

Garner's research specializes in category theory and its applications to logic, topology, geometry, and computer science, including higher categorical structures, monoidal categories, homotopy theory, and algebraic weak factorisation systems. He has secured multiple ARC Discovery Projects, such as 'Structural homotopy theory: a category-theoretic study' (2013–2016), 'Monoidal categories and beyond: new contexts and new applications' (2016–2019), 'Working synthetically in higher categorical structures' (2019–2022), 'Enriched categories: applications in geometry and logic' (2017–ongoing), and sponsorship for 'DE23: New Foundations for Algebraic Geometry' (2023–2026). His key publications include 'Enriched categories as a free cocompletion' (Advances in Mathematics, 2016, with Michael Shulman), 'Lifting accessible model structures' (Journal of Topology, 2020, with Magdalena Kędziorek and Emily Riehl), 'The costructure–cosemantics adjunction for comodels of computational effects' (Mathematical Structures in Computer Science, 2022), 'Cartesian closed varieties I: the classification theorem' (Algebra Universalis, 2024), and 'Functorial aggregation' (Journal of Pure and Applied Algebra, 2025, with D. I. Spivak and A. D. Fairbanks). Garner received the Australian Mathematical Society Medal in 2017 for distinguished research. For teaching excellence, he won the Vice-Chancellor's Learning and Teaching Student-Nominated Award in 2023 and was a Highly Commended Finalist in 2022. He teaches mathematics units like MATH2055 and MATH1007 to large cohorts of engineering and computing students, using a puzzle-solving approach grounded in real-world problems.