Universal Algebra seminar

Ian's short talk: In 1998, in the same paper as their dichotomy conjecture for CSP complexity, Feder and Vardi showed that any constraint satisfaction problem is polynomially equivalent to that of a bipartite graph with constants. In fact, they explain how to construct the graph. This talk is an exploration of which Maltsev conditions satisfied by a relational structure are still satisfied by the graph associated to it via this construction.

Nasir's short talk: A partially ordered semigroup, briefly posemigroup, is

a pair (S,≤) comprising a semigroup S and a partial order ≤ (on S) that is compatible with the binary operation, i.e. for all s₁,s₂,t₁,t₂∈S, (s₁≤t₁,

s₂≤t₂) implies s₁s₂≤t₁t₂. A posemigroup homomorphism is a monotone

semigroup homomorphism. A class of posemigroups is called a variety if it is closed under taking homomorphic images, direct products (endowed with componentwise order) and subposemigroups. Each variety of posemigroups gives rise to a category in natural way. A posemigroup homomorphism f:(S,≤1)→(T,≤2) is called an epimorphism if g∘f=h∘f implies g=h for all posemigroup homomorphisms g,h:(T,≤2)→(U,≤3). Clearly f is an epimorphism in the category of all posemigroups if such is f′:S→T in the category of all semigroups, where f′(s)=f(s) for all s∈S. My aim is to show that the converse of this statement, which may not be true in general, holds in the varieties of absolutely closed semigroups.