
working archive plugin, please!
Over the last two weeks Ive ported all old neverendingbookspost from the last 4 years to a nearly readable format. Some tiny problems remain : a few TeXheavy old posts are still in $…$ format rather than LaTeXrendercompatible (but Ill fix this soon), a few links may turn out to be dead (still have to […]

the modular group and superpotentials (1)
Here I will go over the last post at a more leisurely pace, focussing on a couple of far more trivial examples. Here’s the goal : we want to assign a quiversuperpotential to any subgroup of finite index of the modular group. So fix such a subgroup $\Gamma’ $ of the modular group $\Gamma=PSL_2(\mathbb{Z}) $…

Superpotentials and CalabiYaus
Yesterday, Jan Stienstra gave a talk at theARTS entitled “Quivers, superpotentials and Dimer Models”. He started off by telling that the talk was based on a paper he put on the arXiv Hypergeometric Systems in two Variables, Quivers, Dimers and Dessins d’Enfants but that he was not going to say a thing about dessins but…

Anabelian & Noncommutative Geometry 2
Last time (possibly with help from the survival guide) we have seen that the universal map from the modular group $\Gamma = PSL_2(\mathbb{Z}) $ to its profinite completion $\hat{\Gamma} = \underset{\leftarrow}{lim}~PSL_2(\mathbb{Z})/N $ (limit over all finite index normal subgroups $N $) gives an embedding of the sets of (continuous) simple finite dimensional representations $\mathbf{simp}_c~\hat{\Gamma} \subset…

Anabelian vs. Noncommutative Geometry
This is how my attention was drawn to what I have since termed anabelian algebraic geometry, whose starting point was exactly a study (limited for the moment to characteristic zero) of the action of absolute Galois groups (particularly the groups $Gal(\overline{K}/K) $, where K is an extension of finite type of the prime field) on…

Segal’s formal neighbourhood result
Yesterday, Ed Segal gave a talk at the Arts. His title “Superpotential algebras from 3fold singularities” didnt look too promising to me. And sure enough it was all there again : stringtheory, Dbranes, CalabiYaus, superpotentials, all the pseudophysics babble that spreads virally among the youngest generation of algebraists and geometers. Fortunately, his talk did contain…

Mgeometry (3)
For any finite dimensional Arepresentation S we defined before a character $\chi(S) $ which is an linear functional on the noncommutative functions $\mathfrak{g}_A = A/[A,A]_{vect} $ and defined via $\chi_a(S) = Tr(a  S) $ for all $a \in A $ We would like to have enough such characters to separate simples, that is we…

Mgeometry (1)
Take an affine $\mathbb{C} $algebra A (not necessarily commutative). We will assign to it a strange object called the tangentquiver $\vec{t}~A $, compute it in a few examples and later show how it connects with existing theory and how it can be used. This series of posts can be seen as the promised notes of…

Hexagonal Moonshine (3)
Hexagons keep on popping up in the representation theory of the modular group and its close associates. We have seen before that singularities in 2dimensional representation varieties of the three string braid group $B_3 $ are ‘clanned together’ in hexagons and last time Ive mentioned (in passing) that the representation theory of the modular group…