
Learners and Poly
Brendan Fong, David Spivak and Remy Tuyeras cooked up a vast generalisation of neural networks in their paper Backprop as Functor: A compositional perspective on supervised learning. Here’s a nice introduction to neural networks for category theorists by Bruno Gavranovic. At 1.49m he tries to explain supervised learning with neural networks in one slide. Learners […]

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 $\mathbb{Z}$…

Deep learning and toposes
Judging from this and that paper, deep learning is the string theory of the 2020s for geometers and representation theorists. String theory is the 90s answer to the tears of algebraic geometers worldwide trying to write the "Applications" part of their grant proposals. https://t.co/AboZ5WkPtc — algebraic geometer BLM (@BarbaraFantechi) December 17, 2021 If you want…

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 BCsystem, absolute cyclotomy and the quantized calculus (and which they conjectured previously to…

Alain Connes on his RHproject
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 Comoconference, end of september: Unifying themes in Geometry. In Corona times, virtual conferences…