# Departmental PhD Thesis Exam

Event Information On Braidors: An Analogue of the Theory of Drinfel'd Associators for Braids in an Annulus
13:00 on Wednesday February 19, 2020
14:00 on Wednesday February 19, 2020
BA1210, Bahen Center, 40 St. George St.
Travis Ens
We develop the theory of braidors, an analogue of Drinfel'd's theory of associators in which braids in an annulus are considered rather than braids in a disk. After defining braidors and showing they exist, we prove that a braidor is defined by a single equation, an analogue of a well-known theorem of Furusho [Furusho (2010)] in the case of associators. Next some progress towards an analogue of another key theorem, due to Drinfel'd [Drinfel'd (1991)] in the case of associators, is presented. The desired result in the annular case is that braidors can be constructed degree be degree. Integral to these results are annular versions $\textbf{GT}_a$ and $\textbf{GRT}_a$ of the Grothendieck-Teichm\"uller groups $\textbf{GT}$ and $\textbf{GRT}$ which act faithfully and transitively on the space of braidors.