I work in an area called "Geometric Topology". This is a subject concerned with geometry, fairly generally construed. This includes topics such as manifolds, and knot theory. My specific research tends towards topics such as "spaces of things" like configuration spaces, or spaces of embeddings of one manifold in another. I also enjoy studying the homotopy-types of diffeomorphism groups of manifolds. Recently I've been building a list of the "smallest" triangulated smooth 4-manifolds, as well as a table of knotted 2-spheres in the 4-sphere. I have also been interested in some `applied topology' topics such as persistent homology.

Interests

• Geometric topology
• Manifolds
• Persistent homology
• Knot theory

Faces of UVic Research video

In this video, Ryan talks about his research work in area of topology and how that application is used to look at geometric problems.

Courses

• Fall 2024: 听 听
• Spring 2025: 听
• Summer 2025: