# Category:absolute

• ## The hype cycle of an idea

These three ideas (re)surfaced over the last two decades, claiming to have potential applications to major open problems: (2000) $\mathbb{F}_1$-geometry tries to view $\mathbf{Spec}(\mathbb{Z})$ as a curve over the field with one element, and mimic Weil’s proof of RH for curves over finite fields to prove the Riemann hypothesis. (2012) IUTT, for Inter Universal Teichmuller […]

• ## Smirnov on $\mathbb{F}_1$ and the RH

Wednesday, Alexander Smirnov (Steklov Institute) gave the first talk in the $\mathbb{F}_1$ world seminar. Here’s his title and abstract: Title: The 10th Discriminant and Tensor Powers of $\mathbb{Z}$ “We plan to discuss very shortly certain achievements and disappointments of the $\mathbb{F}_1$-approach. In addition, we will consider a possibility to apply noncommutative tensor powers of $\mathbb{Z}$…

• ## The $\mathbb{F}_1$ World Seminar

For some time I knew it was in the making, now they are ready to launch it: The $\mathbb{F}_1$ World Seminar, an online seminar dedicated to the “field with one element”, and its many connections to areas in mathematics such as arithmetic, geometry, representation theory and combinatorics. The organisers are Jaiung Jun, Oliver Lorscheid, Yuri…

• ## Do we need the sphere spectrum?

Last time I mentioned the talk “From noncommutative geometry to the tropical geometry of the scaling site” by Alain Connes, culminating in the canonical isomorphism (last slide of the talk) Or rather, what is actually proved in his paper with Caterina Consani BC-system, absolute cyclotomy and the quantized calculus (and which they conjectured previously to…

• ## Alain Connes on his RH-project

In recent months, my primary focus was on teaching and family matters, so I make advantage of this Christmas break to catch up with some of the things I’ve missed. Peter Woit’s blog alerted me to the existence of the (virtual) Lake Como-conference, end of september: Unifying themes in Geometry. In Corona times, virtual conferences…

• ## Closing in on Gabriel’s topos?

‘Gabriel’s topos’ (see here) is the conjectural, but still elusive topos from which the validity of the Riemann hypothesis would follow. It is the latest attempt in Alain Connes’ 20 year long quest to tackle the RH (before, he tried the tools of noncommutative geometry and later those offered by the field with one element).…

• ## From the Da Vinci code to Habiro

The Fibonacci sequence reappears a bit later in Dan Brown’s book ‘The Da Vinci Code’ where it is used to login to the bank account of Jacques Sauniere at the fictitious Parisian branch of the Depository Bank of Zurich. Last time we saw that the Hankel matrix of the Fibonacci series $F=(1,1,2,3,5,\dots)$ is invertible over…

• ## From the Da Vinci code to Galois

In The Da Vinci Code, Dan Brown feels he need to bring in a French cryptologist, Sophie Neveu, to explain the mystery behind this series of numbers: 13 – 3 – 2 – 21 – 1 – 1 – 8 – 5 The Fibonacci sequence, 1-1-2-3-5-8-13-21-34-55-89-144-… is such that any number in it is the…

• ## The latest on Mochizuki

Once in every six months there’s a flurry of online excitement about Mochizuki’s alleged proof of the abc-conjecture. It seems to be that time of the year again. The twitter-account of the ever optimistic @math_jin is probably the best source for (positive) news about IUT/ABC. He now announces the latest version of Yamashita’s ‘summary’ of…

• ## How to dismantle scheme theory?

In several of his talks on #IUTeich, Mochizuki argues that usual scheme theory over $\mathbb{Z}$ is not suited to tackle problems such as the ABC-conjecture. The idea appears to be that ABC involves both the additive and multiplicative nature of integers, making rings into ‘2-dimensional objects’ (and clearly we use both ‘dimensions’ in the theory…