$G_2$-instantons on nilpotent Lie groups

Início: 17/11/2023 17:00

Término: 17/11/2023 18:00

Palestrante: Viviana del Barco (Unicamp)

E-mail do Palestrante: delbarc@ime.unicamp.br

Resumo: In this talk we will discuss recent advancements on G${}_2$-instantons on 7-dimensional 2-step nilpotent Lie groups endowed with a left-invariant coclosed G${}_2$-structures. I will present necessary and sufficient conditions for the characteristic connection of the G${}_2$-structure to be an instanton, in terms of the torsion of the G${}_2$-structure, the torsion of the connection and the Lie group structure. These conditions allow to show that the metrics corresponding to the G${}_2$-instantons define a naturally reductive structure on the simply connected 2-step nilpotent Lie group with left-invariant Riemannian metric. This is a joint work with Andrew Clarke and Andrés Moreno.