Colloquium: Monday, November 20, 4 pm. Speaker: Shai Haran (Technion). Title: “Geometry over F1”.

We give two simple generalizations of commutative rings.
They form (co)-complete categories, that contain commutative (semi-) rings (e.g.
f0; 1g ⊆ [0; 1] ⊆ [0; 1) with the usual multiplication x + y := maxfx; yg). But
they also contains the “integers” ZR (and ZC), and the “residue fields” FR (and
FC), of the real (and complex) numbers. Here ZR is the collection of unit L2 balls,
and FR is the collection of spheres augmented with a 0. The initial object is “the
field with one element” F1.