Categorifying Burau representations and categorical dynamics

This talk will describe a construction of algebra objects in some monoidal categories, which allows one to categorify the Burau representations of (non-simply laced type) generalised braid groups. This categorification opens the door to study the dynamics of generalised braid groups through categorical dynamics, similar to the study of dynamics of standard braid groups by viewing it as mapping class groups of some punctured disks. Parallel to the theory of train-tracks by Bestvina-Handel, the talk will show that the categorical entropies can be computed from the Perron-Frobenius eigenvalues of certain matrices obtained through stability conditions closely related to the root systems.

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