Graduate & Undergraduate Student Seminar (GAUSS)
A fundamental question in knot theory is to determine when two given knots are equivalent. Several methods have been developed to study this problem, including tools like the writhe, Kauffman bracket, and HOMFLY polynomial (which includes the Conway and Jones polynomials as special cases). The stunningly remarkable fact is that these same concepts arise naturally in physics from a type of gauge theory known as Chern-Simons theory, which looks to compute topologically invariant quantities using quantum field theory. All of the aforementioned ideas are incredibly deep and are active areas of modern mathematical and theoretical physics research.
With an emphasis on the physics side, the purpose of this talk is to give a very rough overview of how quantum field theory and knot theory are related. While every attempt will be made to distill ideas down as far as possible, this talk will be most easily accessible to those with an advanced mathematical background (e.g., multivariable calculus, abstract algebra/group theory, linear algebra, and smooth manifolds/differential geometry). Of course, all are welcome and encouraged to come regardless of background.