GGT seminar: A Geometric Approach to the Links-Quivers Correspondence for Rational Knots
- Event Type
- Seminar/Symposium
- Sponsor
- Groups, Geometry, and Topology Seminar
- Location
- 347 Altgeld Hall
- Date
- Nov 20, 2025 11:00 am - 12:00 pm
- Speaker
- Jonathan Higgins (Illinois)
- Views
- 13
- Originating Calendar
- Groups, Geometry, and Topology Calendar
- Abstract: The Colored HOMFLY-PT polynomials are an infinite family of link invariants generalizing many other well-known polynomial invariants, such as the Jones polynomial. Although they are generally quite difficult to compute, the Links-Quivers Correspondence conjectures that the generating function for these invariants can be put in a "quiver form" so that computing the entire generating function reduces to computing a quadratic form and two linear forms. The conjecture was previously proved by Wedrich and Stosic for rational knots, but their proof left open how these linear and quadratic forms are related to the geometry of the knot. I answer this question by providing a direct, geometric way to compute them in terms of the punctured plane and its second symmetric product.