Ian Payne, Pure Mathematics Department, University of Waterloo
“The Absorption Theorem and its Proof (Part 1)”
In this first of two lectures, I will start with the definition of an absorbing subalgebra, as well as some useful definitions and observations surrounding them. I then will state, and begin to prove the “absorption theorem” of Barto and Kozik. This theorem helps to give a useful characterization of varieties having a Taylor operation, and has applications to con- straint satisfaction problems. In the second lecture, I will finish the proof of the absorption theorem. Everything presented is from the paper “Absorbing Subalgebras, Cyclic Terms, and the Constraint Satisfaction Problem” by Barto and Kozik.