Monday 16 October 2023, 15:00-16:00, Carslaw 535 Speaker: Damian Lin (Sydney) Title: Virtual Knots and the Gordon-Litherland Linking Form Abstract: We introduce virtual knots, a combinatorial generalisation of the under-crossing and over-crossing information present in classical knot theory, that aren’t subject to the same geometric restrictions. There are also multiple different geometric interpretations of virtual knots as knots on compact orientable surfaces. Specific classes of virtual knots have nice properties, including the alternating virtual knots, for which the Tait graph is well-defined. This allows us to generalise a powerful alternating knot invariant, able to distinguish the mutation classes of alternating knots (Greene 2012). This talk is based on joint work with Hans Boden, Zsuzsanna Dancso and Tilda Wilkinson-Finch.