String Theory Journal Club

In recent years the notion of computational complexity has become the object of intensive study for physicists despite the fact that it is a concept originating from computer science. So why is the physics community so interested in this particular topic and what can we hope to learn from it? In my talk I will briefly address these questions in a general context and then proceed to discuss the measure called Krylov complexity in particular. This measure, although one of many, has become very popular because of its wide range of applicability and computability. I will elaborate on these qualities by reviewing its construction and highlighting certain aspects that in principle make it an interesting probe for any quantum system. Hence, it can be likened to a panopticon from which one can gain access to information about systems ranging from condensed matter to exotic QFTs and possibly holography. Finally, I will present some of the latest advancements and discuss how they shape our current understanding of Krylov complexity and its place in the “zoo” of complexity measures. Online link: meet.google.com/gbj-tmns-err