Computations in low-dimensional topology: quantum knot polynomials and ribbon concordance.

This talk will be divided into two parts. In the first part, we present an algorithm which computes any quantum knot polynomial in time fixed-parameter tractable (FPT) in the treewidth of the knot diagram. Assuming the conjecture that the 2-colored Links—Gould polynomial detects the 3-genus, this gives an FPT algorithm for computing the 3-genus of knots. In the second part, we discuss joint work in progress with Nathan Dunfield and Qiuyu Ren about exploring ribbon concordance using the algorithm by Casson and Long.