
Quiversuperpotentials
It’s been a while, so let’s include a recap : a (transitive) permutation representation of the modular group $\Gamma = PSL_2(\mathbb{Z}) $ is determined by the conjugacy class of a cofinite subgroup $\Lambda \subset \Gamma $, or equivalently, to a dessin d’enfant. We have introduced a quiver (aka an oriented graph) which comes from a…

the modular group and superpotentials (2)
Last time we have that that one can represent (the conjugacy class of) a finite index subgroup of the modular group $\Gamma = PSL_2(\mathbb{Z}) $ by a Farey symbol or by a dessin or by its fundamental domain. Today we will associate a quiver to it. For example, the modular group itself is represented by…

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…

Segalâ€™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…

2006 paper nominees
Here are my nominees for the 2006 paper of the year award in mathematics & mathematical physics : in math.RA : math.RA/0606241 : Notes on Ainfinity algebras, Ainfinity categories and noncommutative geometry. I by Maxim Kontsevich and Yan Soibelman. Here is the abstract : We develop geometric approach to Ainfinity algebras and Ainfinity categories based…