A few quick math/physics items (OK, mostly math…):
- Contributions to next year’s ICM have already been written up by many speakers, and posted on the arXiv. Try this link to find them.
- There’s a wonderful new result from Kevin Costello that he talks about here. A central part of our understanding of the Standard Model is the computation of the beta-function of QCD. The beta-function determines the running of the effective strong coupling with energy, and this has been convincingly tested in many processes over a wide range of energy scales.
The usual way of calculating this is a Feynman diagram calculation that can be found in any QFT textbook that shows how to do calculations in gauge theory. Costello explains how to get the result in a very different way, using the self-dual theory, twistor space, and the Grothendieck-Riemann-Roch theorem.
- There’s a new volume of articles in honor of Gerard Laumon (who passed away on October 4) about algebraic geometry and the Langlands program, available at this website.
- On the Peter Scholze front, in this interview he explains in general terms some of the fundamental ideas he has been pursuing in his recent research, including the motivation of finding new ideas about geometry to describe Spec Z.
This semester at Bonn, he’s pursuing a project of generalizing geometry (lecture notes in progress here) by defining and studying “Gestalten”, which are supposed to be a new sort of geometric object, for which there is “a perfect duality between geometry and algebra!”
For a nice write-up about Scholze’s work on a geometrization of real local Langlands, see here.
At the late March 2026 Seminaire Bourbaki, Scholze will be lecturing on “Geometric Langlands, after Gaitsgory, Raskin, … “
