Noncommutative geometry and the field with one element

School of Mathematics Colloquium
Tuesday, April 27, 2010 - 11:05am for 1 hour (actually 50 minutes)
Skiles 269
Matilde Marcolli – Caltech – matilde@caltech.edu
Stavros Garoufalidis
There are presently different approaches to definealgebraic geometry over the mysterious "field with one element".I will focus on two versions, one by Soule' and one by Borger,that appear to have a direct connection to NoncommutativeGeometry via the quantum statistical mechanics of Q-latticesand the theory of endomotives. I will also relate to endomotivesand Noncommutative Geometry the analytic geometry over F1,as defined by Manin in terms of the Habiro ring.