BYU

Abstract by Brevan Ellefsen

Personal Infomation


Presenter's Name

Brevan Ellefsen

Degree Level

Undergraduate

Abstract Infomation


Department

Mathematics

Faculty Advisor

Mark Hughes

Title

Khovanov Homology and the Jones Polynomial

Abstract

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.