Math Department Colloquium -- Distinguished Speculative First of April Talk

Speaker: Scott Carter (University of South Alabama)

Title: The Role of Knots and Higher Dimensional Knots in Our Understanding of the Quantum World

Abstract: According to the organizers of this event, this talk is meant to be speculative. The title alone satisfies that criterion! Yet, there seem to be at least two conflicting views of matter within our collective consciousness: the discrete and the continuous. Atoms, electrons, quarks, {\it etc.} are discrete particles while the meaning of particle in the first place has to do with a continuum --- the collection of representations of a (product of) unitary groups.

Since the time of Taite and Thompson (Lord Kelvin), and perhaps earlier, matter was thought to be composed of knotted vortices in the aether. Such a model is notoriously wrong, yet some aspects persist. Knotted vortices can be created in the lab via the quantum hall effect. The space-time trace of a particle is a string, and indeed a $4$-dimensional view of the universe suggests that we should examine the interactions of critical events.

So in this talk we start from toy models of particles that are created or annihilated, and that radiate and examine their critical interactions. Those aspects that you would like to consider ``the same," I will consider as isomorphic. And I will then study the isomorphism among them. To continue the speculation, we'll successively project figures to planes and see if the interactions among critical events therein resemble the physical models of reality.

The talk will be informed by pictures.

Bio: Dr. Carter graduated from Yale with a PhD in 1982. After that, he taught at University of Texas, Lake Forrest College and Wayne State University. In 1989, he became a professor of University of South Alabama. Since then, he has been active in the Mobile Math Circle and on Youtube. He was the chair of the Department of Math and Statistics of University of South Alabama from 2003 to 2010. He is currently a managing editor of Journal of Knot Theory and its Ramifications.