Strong Convergence

The first instance of the strong convergence phenomenon was established by Haagerup and Thorbjørnsen in the context of operator algebras more than two decades ago. Since then, the strong convergence phenomenon has emerged naturally in connection with a variety of topics across mathematics, including expander graphs, spectral gaps for manifolds, and constrained minimal surfaces. We present here the first part of Jorge Garza-Vargas’s three-part mini-course on the topic, from our ICM Satellite Conference on Spectral Theory, High-Dimensional Expansion, and Pseudorandomness. The course introduces and motivates the notion of strong convergence, discusses recent proof techniques, and showcases concrete applications. Parts 2 and 3 are available here and here, respectively.