We'll use the regular Number Theory seminar this week to plan a graduate-student reading group in number theory for next semester. The goal is to organize a low-commitment, accessible reading group for graduate students at all career stages. Everyone is welcome to join, and we are in the market for suggested topics and sources!
It is well-known that a function (of arity ) preserves an equivalence or a quasiorder relation if (and only if) each unary polynomial function preserves which can be obtained from by substituting constants at all but one arguments. Thus the polymorphism clone Pol is completely determined by the endomorphism monoid End. We ask which other relations and which monoids of unary mappings may have the same property. We introduce so-called generalized quasiorders which play a central role for answering these questions (moreover, they lead to new algebraic notions generalizing, e.g., affine completeness).
Join work with Danica Jakubikova-Studenovska (Kosice, Slovakia) and Sandor Radeleczki (Miskolc, Hungary)