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DTSTART:19700329T010000
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UID:1213
SUMMARY:Pure Mathematics Seminar: Caroline Series
DESCRIPTION:Representations of the free group into SL(2,C): discreteness and the Bowditch conjecture\n\nIt is an old problem to determine when a representation of the free group F2 on two generators into SL(2,C) is free and discrete. Such a representation is determined up to conjugacy by the traces of any triple (X,Y,XY), where X,Y are a pair of generators.\n\nThe traces of all possible triples can be neatly calculated by arranging them as the vertices of a trivalent tree, dual to the Farey tesselation of the hyperbolic plane. In 1997, Bowditch introduced a condition on traces which, using some ingenious manipulations on the tree, gave a purely combinatorial proof of McShane's identity, an important result about traces previously only known for discrete groups.\n\nThe precise relationship of Bowditch's condition to discrete groups remains rather mysterious. We present some surprising computer graphics which compare the set of representations which satisfy a generalised version of Bowditch's condition with those which are free and discrete. This is joint work with Ser Peow Tan and Yasushi Yamasita.
DTSTART:20131106T150000
DTEND:20131106T160000
LOCATION:A54, Postgraduate Statistics Centre Lecture Theatre
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