In this talk we will discuss a recent line of study establishing the 2-to-2 games conjecture, albeit with imperfect completeness.
At the heart of the approach lies an object called the Grassmann Graph, and a certain linearity test on it.
This leads to the study of edge expansion in this graph, and in particular, the study of (small) sets of vertices in the Grassmann Graph, whose edge expansion is bounded away from 1.
NOTE: This talk is streamed via Google Hangouts.