GHAIA Seminars

Transfer of knowledge open only to the members of the project

In this seminar we will talk about two generalizations of Jordan triple systems: the triple systems originally introduced by I. L. Kantor in the 1970s and the contemporary supersymmetric Jordan triple systems. We will describe their relation with graded Lie (super)algebras with involutions via the TKK construction and discuss their classification. Explicit examples will be given, both in the finite-dimensional and infinite-dimensional case.

Complex projective structures with branch points arise naturally in the study of a certain class of linear rank 2 ODEs on Riemann surfaces. We focus on the genus 2 case, where these structures can be conveniently described in terms of bubbling, i.e. connected sum with the Riemann sphere. This geometric point of view allows for an effective description of the symmetries and deformations of these geometric structures. We will present an application to the study of the Riemann-Hilbert map for the aforementioned class of ODEs.