Spring 2024

Speaker: Rotislav Akhmechet (Columbia University)

Room:  AB1/L06

Time:  March 13 from 11:30-12:30

Title:  Knots, polynomials, homology, and beyond

Abstract: A fundamental question in knot theory is to decide whether two seemingly different knots are actually distinct. This is typically accomplished via knot invariants, which are objects (for instance: numbers, polynomials, vector spaces) that do not change if we represent the same knot in a different way. Beyond distinguishing knots from each other, knot invariants often have rich structures and interconnected properties that can reveal subtle topological information. I will give an overview of knot invariants focusing on the Jones polynomial and Khovanov's seminal categorification of the Jones polynomial. Structural properties, further refinements, and some open questions will be discussed.