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Petar Markovic: An overview of colored edge theory

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Wednesday, 7. December 2022, 10:10 - 11:00
In this lecture I will survey what is left in the colored edge theory by Bulatov, that we didn't cover in the previous lectures. The topics I will expose are rectangularity of compatible relations when restricted to the as-maximal components, the quasi-2-decomposability and the existence of a quasi-majority term, a stronger rectangularity for the compatible relations when the algebra is maximal-generated, connections between colored edges and Tame Congruence Theory concepts, in particular subtraces, and finally the definitions and initial results about separation of congruence covers.
The final part plays a large part in the Dichotomy proof. In Bulatov's papers, separation of congruence intervals is mostly considered in an extremely narrow situation which arises during the tractability algorithm. The reason for this is that separability is not symmetric, and Bulatov needs it to be, so he considers only the narrowest possible situation where he proves a weak symmetry result. However, the initial ttwo results on separation are general enough to be applicable elsewhere and those will be surveyed.

 
The lecture will be in the Riesz lecture room.
 

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