The shape of all prime numbers, 1 and 2 (by L. Le Bruyn)

Our knowledge of the geometric shape of prime numbers changed dramatically over the last century. The most common point of view, dating back to Dedekind and Kronecker, is to picture them just as points on a line. In the early 60ties, Grothendieck and his gang developed étale cohomology, forcing us to view prime numbers as knots in 3-space. In recent years,  Ŧ₁-geometry suggests that the shape of all prime numbers may be infinitely more complex.

 

 

-FIRST TALK-

In the first talk I’ll give a low-tech account of this story, focusing on the philosophy and motivation of Ŧ₁-geometry. I will give a new proposal, in the spirit of Jim Borger’s approach via λ-rings, to view additional structure on rings as descent data from the integers ℤ to the field with one element Ŧ₁.

 

-SECOND TALK-

In the second talk I’ll indicate how this approach fits in nicely with Alexander Smirnov’s proposed attack on the ABC-conjecture via Ŧ₁-geometry and (if time allows) a question posed by Yuri I. Manin in the previous seminar on the motivic interpretation of the local Γ-factor at complex arithmetic infinity.

The next Ŧ₁-seminar (December 21, 2017)

The next Ŧ₁-seminars will take place in December 2017. The speaker will be Lieven Le Bruyn, from University of Antwerp.

WHEN ?: The seminar is scheduled for Thursday December 21, 2017.

WHERE ?: Department of Mathematics, Ghent University, Krijgslaan 281, Building S25, Ghent, Belgium.

SCHEDULE:

13:30 – 14:00: Coffee break (Entrance hall, Building S25)

14:00 – 14:15: Blitzing through Ŧ₁-theory (by K. Thas)
14:20 – 15:10: The shape of all prime numbers, 1 [ABSTRACT] (by L. Le Bruyn)

15:10 – !5:25: Coffee break (Entrance hall, Building S25)

15:25 – 16:15: The shape of all prime numbers, 2 [ABSTRACT] (by L. Le Bruyn)

16:15 – 17:15: Reception (Entrance hall, Building S25)

All lectures will take place in Room “Emmy Noether,” Building S25.