Topology Seminar

Sam Nelson will wow us with his maths.

Robert Bowden will tell us fantastic things he did at PSU.

Jim Hoste will do an interpretive knot dance.

Title: Untying Knots with Neural Nets Abstract: Neural networks can transform 3-dimensional data in a manner reminiscent of an ambient isotopy. With some modifications, a neural network can be trained […]

In this talk I will recount the history of my knot theory-based music project and show an example of my method for creating music from knot homsets.

M. Niebrzydowski and J. H. Przytycki defined a Kauffman bracket magma and constructed the invariant P of framed links in 3-space. The invariant is closely related to the Kauffman bracket […]

(Joint with Ichihara, Jong, and Saito). We show that two-bridge knots admit no purely cosmetic surgeries, ie no pair of distinct Dehn surgeries on such a knot produce 3-manifolds that […]

We talk about building knots using mosaics which were as introduced as a way of modeling quantum knots by Lomonaco and Kauffman and a newer variant, hexagonal mosaics, introduced by […]

The Jones polynomial is an invariant of knots in R^3. Following a proposal of Witten, it was extended to knots in 3-manifolds by Reshetikhin-Turaev using quantum groups. Khovanov homology is […]

Skein modules were introduced by Jozef H. Przytycki as generalisations of the Jones and HOMFLYPT polynomial link invariants in the 3-sphere to arbitrary 3-manifolds. The Kauffman bracket skein module (KBSM) […]

Convex real projective structures generalize hyperbolic structures in a rich way. We will discuss a class of manifolds introduced by Cooper Long and Tillmann, which include finite-volume cusped hyperbolic manifolds […]