Pro-nilsystems play a central role in the inverse theory of uniformity seminorms in ergodic theory and additive combinatorics. In this talk, I will discuss the stability of this class of dynamical systems under taking factors. More precisely, I will explain a direct proof that any factor of an ergodic $k$-step pro-nilsystem is again a $k$-step pro-nilsystem. The main new ingredient is a local rigidity result for ergodic self-joinings of nilsystems: any ergodic self-joining sufficiently close to the diagonal joining is in fact the graph joining of an automorphism. The key geometric input is a "no small subnilmanifolds" lemma. This is based on joint work with Pauwel Van Den Eeckhaut.
Meeting ID: 852 4277 3200 Passcode: 103121