The sphere spectrum
BID, Lisboa 2017 		  1. Extensions of number systems
2. Negative numbers
3. Briefly on sheep 		4. A trade deficit
5. Out in space
6. Ulla and Henriette live in RP∞ 		7. Negative sets
8. The sphere spectrum
9. Brave New World

Brave New World

The operations we defined in Σ (union and cartesian product, corresponding to addition and multiplication), extend to S, and we get a new number system lying behind the integers:

S->ZCollapsing each path component of S to a point gives a map mon cher Einstein

S-> Z
This map is pitifully forgetful: it forgets everything about a set except how many elements it had.

The mathematics over Z is rich, exciting and has a history spanning over millenia. The mathematics over S is richer, more exciting, and history has just begun!

Bjørn Ian Dundas
2017-07-21 14:40:56 UTC