Noncommutative geometry and the field with one element

Series: 
School of Mathematics Colloquium
Tuesday, April 27, 2010 - 11:05
1 hour (actually 50 minutes)
Location: 
Skiles 269
,  
Caltech
,  
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.