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Virtual knots are generalizations of classical knots that contain an additional type of crossing called a virtual crossing, and they can be represented as knots on surfaces. Quandle coloring can be extended to virtual knot diagrams using virtual quandles, which use a quandle automorphism to describe the behavior at virtual crossings. Most extensions of the Boltzmann weight and quandle state-sum invariant to virtual knots ignore possible contributions from the virtual crossings. In this talk we create new virtual link invariants using virtual quandles. We also present a new virtual quandle cohomology theory that describes the contribution to the Boltzmann weight from virtual crossings. We use that cohomology theory to create a categorification of virtual link colorings in the form of the virtual quandle cohomology quiver representation.

https://ucdavis.zoom.us/j/93247351709?pwd=USncSfx1MsPLei9aCXlEdJZhURFQLn.1 Meeting ID: 932 4735 1709 Passcode: 073821