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Abstract: This talk will focus on the Lie algebra sl(2) of 2 x 2 matrices of trace zero and a choice of basis for it that makes transparent connections with the modular group, the braid group on 3 strands, hyperbolic space, automorphisms of the Poincare disk, Tits buildings, a geometry over the field of one element, and more.\par
This talk will be accessible to graduate students.
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