Abstract by Brevan Ellefsen
Khovanov Homology and the Jones Polynomial
Khovanov Homology exemplifies the idea of categorification, which strives to take concrete structures and algebraically "lift" them to gain additional structure and insights. In particular, Khovanov Homology categorifies the Jones Polynomial, a classical and easily calculated invariant of Knot Theory allowing us to distinguish many knots. A brief and relatively elementary introduction to Khovanov Homology will be given, followed by a discussion on some recent results and its connections to the Jones Polynomial.