Research Interests: Geometric Topology, Knot Theory, Group Theory
I am interested in link concordance and groups related to the study of link concordance (such as the knot concordance group, the pure braid group, and the string link concordance group). My work addresses these topics using generalizations of classical techniques related to combinatorial group theory as well as modern gauge theoretic tools from Heegaard Floer homology. Additionally, I am curious about questions involving the mapping class group and the various flavors of homology cobordism group. I am a member of NAM, the AMS, and the AWM and I am a Math Alliance mentor.
Current and Upcoming Activities:
Notes and Videos of Previous Talks:
You can find notes from a talk I gave on my paper "An Analogue of Milnor's Invariants for Knots in 3-Manifolds" at the Virginia Topology Conference at UVA here.
A while back, I gave an undergraduate colloquium for math and physics majors at Andrews University about cobordism groups, you can find the video here.