***Special Dynamical Systems and Ergodic Theory Seminar***

Furstenberg's proof of Szemeredi's theorem introduced the Correspondence Principle, a general technique for translating a combinatorial problem into a dynamical one. While the original formulation suffices for certain patterns, including arithmetic progressions and some infinite configurations, higher order generalizations have required refinements of these tools. We discuss the new techniques introduced in joint work with Moreira, Richter, and Robertson that are used to show the existence of infinite patterns in large sets of integers.