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### Towards an exceptional knot polynomial

**Geometry/Topology**

Speaker: | Dylan Thurston, Indiana University |

Related Webpage: | https://www.math.ucdavis.edu/research/seminars/thurston/ |

Location: | 1147 MSB |

Start time: | Thu, May 4 2017, 12:10PM |

We find a single two-parameter skein relation on trivalent graphs, the quantum exceptional relation, that specializes to a skein relation

associated to each exceptional Lie algebra. Based on Deligne's

conjecture for the (classical) exceptional conjecture, we conjecture

that this relation determines a new two-variable quantum execptional

polynomial. We can compute this two-variable polynomial for all knots

with up to 12 crossings, in particular determining (unconditionally)

the 1-variable polynomial associated to these knots for any of the

exceptional Lie algebras.

This is joint work with Scott Morrison and Noah Snyder.