Recurrence for IP Systems with Polynomial Wildcards
Shortly after Szemeredi proved that a set of natural numbers with positive upper density contains arbitrarily long arithmetic progressions, Furstenberg gave a new proof using ergodic theory. This major event gave rise to the field of combinatorial ergodic theory, in which problems motivated by additive combinatorics are addressed with ergodic theory. In this talk we give a brief survey of some of the successes in the field, leading into a description of an interesting, yet still unproved result, which would provide a generalization of many earlier results.