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Dynamics of braid groups and slicings

Oded Yacobi, University of Sydney
Tuesday, October 17, 2023 - 2:30pm to 3:20pm
PDL C-38
Abstract: The braid group B_n on n strands is an important mathematical object with interesting connections to many pure and applied areas, such as fluid mixing, physics, topology and representation theory. Accordingly, one can study B_n from a variety of perspectives. For example, algebraically the Burau representation of B_n is a major player with applications in knot theory and symplectic topology. Dynamically, the realisation of B_n as the mapping class group of the punctured disc leads to the study of entropy of braids. It is an interesting question how to link these two approaches. In this talk we'll explain a result in this direction: braids of entropy 0 can be detected homologically from the categorical Burau representation as those braids which are ``slicing-perverse''. This is a new notion that incorporates stability conditions into the definition of perverse equivalences. Based on joint work with Ed Heng (IHES) and Tony Licata (ANU).
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