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# Calvin McPhail-Snyder, Duke – Geometric Methods in Representation Theory Seminar

## October 1, 2021 @ 4:00 pm - 5:00 pm

Title: *Quantum invariants from unrestricted quantum groups*

Abstract: Quantum groups are a central part of the construction of quantum invariants of knots, links, and 3-manifolds. Existing work focuses mainly on the case where the quantization parameter q is generic, or on the semisimplified theory at q a root of unity. In this talk, I will discuss how to construct invariants of knots (and links) using the non-semisimple part of unrestricted quantum sl_2 at a root of unity. These “holonomy invariants” turn out to be very geometric: they depend on the extra data of a map from π_1 of the knot complement to SL_2(C), which is essentially a choice of hyperbolic structure.