Date:
Sun, 28/09/202514:30-15:30
Location:
Zoom
Title: Quandle-coloring arithmetic links
Abstract:
The étale topology, and subsequently the étale homotopy type, were developed in order to borrow further and finer tools from topology, and apply them to better describe algebraic and arithmetic objects. Originally of interest in studying varieties over fields, an observation of Barry Mazur’s interprets prime numbers as knots. Squarefree integers are similarly interpreted as links.
An involutive quandle, or kei, is a type of algebraic structure well-suited for producing numerical invariants of knots and links, counting what are classically known as colorings. In this project we define an arithmetic analogue of these coloring invariants, producing for each finite kei an arithmetic function. We conjecture that the average asymptotic order of these functions may be predicted to some extent using observations regarding the colorings of closures of random braids.