Month: September 2021

Welded Tangles and the Kashiwara-Vergne Groups

| chrisman.76

Zsuzsanna Dancso (The University of Sydney)

In this talk I will explain a general method of “translating” between a certain type of problem in topology, and solving equations in graded spaces in (quantum) algebra. I’ll talk through several applications of this method from the 90’s to today: Drinfel’d associators and parenthesised braids, Grothendieck-Teichmuller groups, welded tangles and the Alekseev-Enriquez-Torossian formulation of the Kashiwara-Vergne equations, and most recently, a topological description of the Kashiwara-Vergne groups. The “recent” portion of the talk is based on joint work with Iva Halacheva and Marcy Robertson (arXiv: 2106.02373), and joint work with Dror Bar-Natan (arXiv: 1405.1955).

Cocycle Enhancements of Psyquandle Counting Invariants

| chrisman.76

Jose Ceniceros (Hamilton College)

In this talk we discuss pseudoknots and singular knots. Specifically, we discuss psyquandles and their application to oriented pseudoknots and oriented singular knots. Additionally, we bring cocycle enhancement theory to the case of psyquandles to define enhancements of the psyquandle counting invariant via pairs of a biquandle 2-cocycle and a new function. As an application, we define a single-variable polynomial invariant of both oriented pseudoknots and oriented singular knots.