[AGC seminar] Tuomas Kelomäki | Finiteness result on Jones polynomials via categorified projectors | Mon 25.5. at 14:15

[Aalto Algebra, Geometry and Combinatorics Seminar]

We would like to invite you to the last talk of the spring in the Aalto AGC (Algebra, Geometry and Combinatorics) Seminar!

The talk is on
Mon 25.5. at 14:15-15:00
in
M3, Otakaari 1

The speaker is Tuomas Kelomäki

Title: Finiteness result on Jones polynomials via categorified projectors

Abstract: We will begin introducing knots, braids and the knot invariant Jones polynomial J(K). Following up, we present a fairly simple finiteness result: any fixed number of the lowest degree terms of J(K) on positive braids on any fixed number of strands gives a finite set of polynomials. (Moreover, these terms can be deduced in linear time.)

The proof is obtained by transforming the existing category theoretical limits from the literature into limits on a metric space. More concretely, we make use of the computations of Rozansky and Islambouli-Willis on categorified Jones-Wenzl projectors. Khovanov-analogues of the result are also discussed.

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