Algebra Seminar, Title of the talk: *Quantized annular Khovanov homology*, University of Sydney, November 30, 2018

Abstract: In the talk I will explain how one can quantize the annular Khovanov homology to get a new triply graded homology theory for annular links which is strictly functorial with respect to annular cobordisms. This theory carries the action of the quantum sl(2) intertwining the action by cobordisms and provides non-trivial invariants of 2-knots. Moreover, in the quantized annular setting the infinite Cooper-Krushkal complex categorifing the Jones-Wenzl projector becomes finite and homotopic to the Khovanov complex for the colored Jones. Joint work with M. Hogancamp, K. Putyra and S. Wehrli.