معرفی
Hans U. Boden is a Professor in the Department of Mathematics & Statistics at McMaster University's Faculty of Science. His research focuses on low-dimensional topology, gauge theory, and knot theory with emphasis on virtual knots, braid theory, and moduli spaces. Current teaching includes Math 2X03, Math 4E03, and iSci 2A18 as of the 2022-2023 academic year.
His research interests center on gauge theory and low-dimensional topology, specifically investigating knots, links, braids and their invariants, moduli spaces of flat connections over 3-manifolds, and moduli spaces of vector bundles over Riemann surfaces. Recent work includes collaborations on virtual knot concordance, alternating links in thickened surfaces, and braid representatives minimizing simple walks with student Matthew Shimoda.
Analysis of his recent publications (2019-2025) reveals a strong trend toward virtual knot theory and surface embeddings, with significant contributions to alternating virtual links, generalized Tait conjectures, and concordance invariants. His work bridges combinatorial topology with geometric structures, frequently employing computational methods like SageMath for braid analysis.
He has co-edited three major books: Gauge Theory and Low-Dimensional Topology: Progress and Interaction (2022), Chern Simons Gauge Theory: 20 years after (2011), and Geometry and Topology of Manifolds (2005).
- Supervised 22+ theses including PhDs by Jie Chen (2023), Homayun Karimi (2018), and Lindsay White (2016)
- Mentored undergraduate researchers through USRA projects and Fields Institute summer programs
- Collaborated with international researchers including Chris Herald, Paul Kirk, and Homayun Karimi
His research group maintains active projects in knot tabulation, virtual knot invariants, and computational topology, with recent work on mutation of surface graphs and minimal crossing diagrams. The group utilizes both theoretical approaches and computational tools like SageMath for knot analysis.
