The 2-to-1 games conjecture is the weaker sibling of the famous and important Unique-games conjecture of [Khot02]. A recent sequence of four papers resolved a version of that former conjecture, which might count as a step towards a proof of the Unique-games conjecture, and in any case invalidates some approaches for refuting it. The proof relies crucially on some Expansion properties of the Grassmann-graph, an object that to our knowledge was not studied before in the context of theoretical Computer Science. In this talk I will explain the 2-to-1 and the Unique-games conjectures and their implications, the Grassman graph and its relevance, and hopefully also some key ideas of the proofs. |