The latest talk of Alain Connes on absolute geometry
Among the many different approaches to $\mathbb{F}_1$ proposed in the literature, one of the most serious is the long-running program of Alain Connes, building on ideas developed with Consani and other collaborators over several decades. I received this video in a message from René Slabbekoorn and wanted to share it here for anyone interested! It's the latest talk of Connes, delivered at the Fundamental Geometries conferences in Bologna this summer, and it gives a nice overview of where this research programme currently stands, with connections to positivity, explicit formulas, ideas of Scholze, and some strange numerics of spectral triples reproducing some part of the Riemann spectrum to very high accuracy.
On the absolute geometry of Spec Z — Alain Connes
Alain Connes is Professor Emeritus at the Collège de France and IHES. Awards include the Fields Medal (1982), the Crafoord Prize (2001) and the CNRS Gold Medal (2004).

