Segal's Burnside ring conjecture, or, more briefly, the Segal conjecture, is a theorem in homotopy theory, a branch of mathematics. The theorem relates the Burnside ring of a finite group G to the stable cohomotopy of the classifying space BG. The conjecture was made by Graeme Segal and proved by Gunnar Carlsson. As of 2006, this statement is still commonly referred to as the Segal conjecture, even though it now has the status of a theorem.