Mathematics Colloquia and Seminars

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Vassiliev invariants are finite-type invariants for knots. They are for knots what polynomial functions are for the integers: those functions that have a vanishing finite difference of some order. Like polynomials, Vassiliev invariants can be odd or even. One believable conjecture is that Vassiliev invariants distinguish all knots. Another believable conjecture is that there are no odd Vassiliev invariants. The two conjectures cannot both be true. In this talk I will sketch a proof that there are no odd Vassiliev invariants up to four loops, which is partial evidence that there aren't any at all.