Apr 18, 2012

Absolute Arithmetic at the 6th European Congress of Mathematics !

Posted by in levels, media, news, research No comments

The mini-symposium “Absolute Arithmetic and -Geometry” is part of the official scientific programme of the prestigious quadrennial European Congress of Mathematics (July 2-7 2012, Krakow, Poland). This conference is widely considered to be one of the most important mathematical gatherings around. The general character of the programme provides attendees with a unique chance of an [...]

Jan 25, 2012

Scheme theory over the field of characteristic one

Posted by in Deitmar2004, media, Tits1957, undergraduate No comments

Second part in a series which I gave at a seminar in Ghent (April 28, 2011): “Scheme theory over the field of characteristic one”. (The first part being “Introduction to Absolute Arithmetic”.)

Sep 21, 2011

Introduction to Absolute Arithmetic

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This is part 1 of a series of two lectures which I recently gave at a seminar in Ghent (April 28, 2011): “Introduction to Absolute Arithmetic”.

Feb 11, 2011


Posted by in levels, library, media, papers, research No comments

Here is the recently published paper “The hyperring of adèle classes” (by Connes and Consani). ConnesConsani2011

Oct 16, 2008

noncommutative F_un geometry (2)

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Last time, we tried to generalize the Connes-Consani approach to the noncommutative world but didn’t specify what we meant by noncommutative varieties or schemes and how they were related to Grothendieck’s dessins d’enfants. That’s what we will do today.

Oct 13, 2008

noncommutative F_un geometry (1)

Posted by in Connes-Consani2008, research 4 comments

It is perhaps surprising that Alain Connes and Katia Consani, two icons of noncommutative geometry, restrict themselves to define commutative algebraic geometry over the field with one element. Remains the fact that their approach screams for a noncommutative extension.

Oct 12, 2008

Andre Weil on the Riemann hypothesis

Posted by in featured, outreach 7 comments

Don’t be fooled by introductory remarks to the effect that ‘the field with one element was conceived by Jacques Tits…’ Let’s have it out into the open : F_un mathematics’ goal is no less than proving the Riemann Hypothesis.

Oct 12, 2008

F_un and group representations

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Grothendieck’s anabelian geometry is an example of noncommutative F_un geometry. Javier starts this series with ramblings on how the folklore about F_un can be used to relate linear and permutation representations of finite groups.

Oct 10, 2008

Connes-Consani for undergraduates (3)

Posted by in Connes-Consani2008, undergraduate 1 comment

Alain Connes and Katia Consani arXived the paper “On the notion of geometry over F_un” in which they refine and simplify Soule’s approach. This series tries to explain their construction to non-specialists in algebraic geometry.

Oct 9, 2008

Gadgets a la Soulé

Posted by in graduate, Soule2004 3 comments

Inspired by the equivalent definition of a scheme as a particular kind of functor, Soulé gives his definition of a gadget over F_un as a couple consisting on a functor, that takes the rôle of the functor of points, and an algebra, which encodes a ‘topology at infinity’ and gives us the extra information that is missing in the functor.