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Seminar

New quantum invariants and knot fiberedness

Speaker
Lara San Martin Suarez, CalTech
Date
Tue, Apr 7 2026, 4:00pm
Location
383N
red knot logo

What do quantum invariants know about knot geometry? Gauge-theoretic invariants, such as knot Floer homology, detect geometric features. However, analogous results for quantum invariants, including the Jones polynomial and its categorification, Khovanov homology, are largely missing. In this talk, I will discuss a relation between the quantum invariant $F_K$, conjectured by Gukov–Manolescu and studied by Park, and knot fiberedness. As an application, we uncover a connection between $\mathfrak{sl}(2)$ quantum invariants and knot geometry, study new $q$-series associated to knots, and observe an unexpected parallel between these $q$-series and extremal knot Floer homology. Based on joint work with Paul Orland, Toby Saunders-A'Court and Josef Svoboda.