Andrew Booker: My converse theorem obsession

In January last year, Min Lee and I hosted a Heilbronn Focused Research Workshop on the "Sarnak Rigidity Conjecture". I will introduce this conjecture and explain why it's hopelessly difficult to make progress on, before turning to some related problems concerned with "converse theorems" in the theory of modular forms that turned out to be more tractable. There will be heavy helpings of philosophy and also some theorems. This is joint work with S. Bettin, J. W. Bober, B. Conrey, M. Lee, G. Molteni, T. Oliver, D. J. Platt, and R. S. Steiner.