FIELD Math:Geometry May 12 (Thu), 2022 10:00-11:00 Online Henry, Guillermo Shin, Jinwoo Universidad de Buenos Aires Solutions of the Yamabe equation induced by subgroups of isometries and isoparametric functions Given a closed $n-$dimensional Riemannian manifold $(M,g)$ with scalar curvature $s_g$. We say that $u$ is a solution of the Yamabe equation if for some constant $c$ it holds $$\frac{4(n-1)}{(n-2)}\Delta_g u+s_gu=c|u|^{\frac{4}{n+2}}u.$$The solutions of this equation are interesting because they are related with metrics of constant scalar curvature in the conformal class of $g$. In this talk we are going to discuss some results on the existence of positive and sign-changing solutions of the Yamabe equation obtained by considering either the action of a subgroup of isometries or an isoparametric foliation.