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Motivated by some ideas in subfactors and conformal field theory we construct families of unitary representations of groups of piecewise-linear homeomorphisms of the circle and the interval. Special cases reveal a way to construct all knots and links from Thompson's groups F and T.
About the speaker
Prof. Jones is currently Stevenson Distinguished Professor at Vanderbilt University, after many years on the faculty of UC Berkeley. Among many honours, he is a recipient of the Fields Medal (1990), a Vice President of the International Guild of Knot Tyers (due to his work on knot theory), a Knight Companion of the New Zealand Order of Merit, a Fellow of the Royal Society and current Vice President of the International Mathematical Union. See his Wikipedia page for more info.