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Braids and Applications

Fast algorithmic construction of quasi-geodesics

speaker: Bertold Wiest (Laboratoire de Mathématiques, Université de Rennes 1)

abstract: This talk is about work in progress with Sandrine Caruso. The aim is to prove that the transmission-relaxation algorithm of Dynnikov and myself can be used to produce, in quadratic time, quasi-geodesics not only in the braid group, but also in Teichmüller space and in the pants complex. Applications include (1) a polynomial time algorithm for finding quasi-geodesic sigma-consistent braid words (in the sense of Dehornoy) and (2) a polynomial time solution to the conjugacy problem in the four-strand braid group. Our work uses no Garside theory, and much of it may generalize to other mapping class groups.

timetable:
Thu 23 Jun, 11:00 - 12:00, Aula Dini
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