Abstract:

Starting from the basics of knot theory, I'll explain why I care about knots living in more general spaces than R^3. We will see how well-known and more recent invariants extend at various costs, with connections from quantum physics to mapping class groups. When the extension is too easy -- namely, for Khovanov homology -- I will explain how surface specific features help refine the invariants, a result I proved with Paul Wedrich during my last visit to the MSI.

Afternoon tea will be provided at 3:30pm