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I study low-dimensional topology and focus on the intersections between hyperbolic geometry, knot theory and triangulations. Broadly speaking, I study 3-dimensional objects. More concretely, I focus on classifying and understanding 3-dimensional spaces called 3-manifolds. These spaces all have the property that the neighbourhood of a point in the space ``looks like'' a 3-dimensional ball. Also, every 3-manifold can be decomposed into tetrahedra, and this gives a combinatorial description of that 3-manifold. However, creating fast and rigourous classification schemes for 3-manifolds can be a challenge because the combinatorial description of a particular manifold can be horrible (e.g. lots of tetrahedra). I also have particular interest in how 3-manifolds are related to each other. There are two ways in which this can happen. The first way is if two manifolds are commensurable i.e. they share a common finite sheeted cover. The second way is if two manifolds are related via a Dehn surgery. That's a fast and loose description of what I do. A list of this work with short descriptions, questions, and slides is available here. |
Curriculum vita (pdf). Updated January 2019.