The Tait conjectures for classical, virtual, and welded knots

Speaker: Professor Hans Boden
Affiliation: McMaster University (Canada)

Abstract

The Tait conjectures were originally posed in the 1900s but remained open for nearly 100 years. They were ultimately resolved in the late 1980s using the then new Jones polynomial. In a more recent development, Josh Greene found a geometric characterization of alternating knots as those that simultaneously bound positive and negative definite spanning surfaces, and he used this to give a new proof of the Tait conjectures. In this talk, I will survey some results obtained by adapting these methods to knots in thickened surfaces and to virtual knots.