*Everyone is welcome to attend. Refreshments will be served in the Math Lounge before the exam.*

Wednesday, February 19, 2020

1:00 p.m.

BA1210

PhD Candidate: Travis Ens

Supervisor: Dror Bar-Natan

Thesis title: On Braidors: An Analogue of the Theory of Drinfel’d Associators for Braids in

an Annulus

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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.

A copy of the thesis can be found here: ens_thesis

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