David Richerby AN EFFECTIVE DICHOTOMY FOR THE COUNTING CONSTRAINT SATISFACTION PROBLEM Bulatov (2008) gave a dichotomy for the counting constraint satisfaction problem #CSP. A problem from #CSP is characterised by a constraint language, a fixed, finite set of relations over a finite domain and instances use these relations to constrain the values taken by variables. Bulatov showed that the problem of counting the satisfying assignments of instances of any problem from #CSP is either in polynomial time (FP) or is #P-complete, depending on the structure of the constraint language. Understanding his proof requires a secure grasp of the universal algebra techniques he uses. We give an elementary proof of the dichotomy, based on succinct representations, which we call 'frames', of a class of highly structured relations, which we call 'strongly rectangular'. We show that these are precisely the relations which are invariant under a Mal'tsev polymorphism. En route, we simplify a decision algorithm for strongly rectangular constraint languages, due to Bulatov and Dalmau (2006). We establish a new criterion for the #CSP dichotomy, which we call 'strong balance', and we prove that this property is decidable -- in fact, in NP. Thus, we show that the dichotomy is effective, resolving the most important open question from Bulatov's work. The talk will require no knowledge of universal algebra and should be accessible to people without any detailed knowledge of the constraint satisfaction problem.