Basic Notions: Jef Laga (Cambridge) - The geometry of simple Lie algebras, with applications to arithmetic statistics II

Thu, 12/05/202216:00-17:15
Link to recording of first talk:

Link to recording of second talk:

Dynkin diagrams of type ADE are the solution to a plethora of classification problems in mathematics, and it is an interesting question to find more direct relations between these different classifications.
In the first talk, I will give an overview of such ADE correspondences and focus on a theorem of Grothendieck and Brieskorn, which relates the geometry of the nilpotent cone of an ADE Lie algebra to the simple surface singularity of the corresponding type.
In the second talk, I will discuss how a graded analogue of this result can be used to obtain statistical information concerning rational points on certain algebraic curves, generalising the celebrated works of Bhargava and his collaborators on average ranks of elliptic curves.