Mathematics Colloquia and Seminars

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Description

I will start from basic knot theory to define the Jones polynomial as a state sum, then define and explore Khovanov homology, with a bit of both specific and general computations. Two main goals, if I can get to them, are to present a proposition about the homology of the knot mirror and to explore the homology of some simple classes of knots. If all goes as planned, most of it will be understandable, and all of it should be at least somewhat interesting, to anyone knowing elementary abstract algebra, though familiarity with basic homology will be useful. In addition to the technical details, I will try to give some perspective as to where this stands in the web of mathematics