FIELD Math:Analysis January 25 (Mon), 2021 14:00-16:00 Online Kim, Seunghyeok Jeong, In-Jee ÇÑ¾ç´ëÇÐ±³ Infinite-time blowing-up solutions to small perturbations of the Yamabe flow Under the validity of the positive mass theorem, the Yamabe flow on a smooth compact Riemannian manifold $M$ of dimension $N ¡Ã 3$ is known to exist for all time $t$ and converges to a metric of constant scalar curvature as $t \to \infty$. We show that if a suitable perturbation, which can be made arbitrarily small and smooth, is imposed on the linear term of the Yamabe flow on $M$, the resulting flow blow-ups at the infinite time, forming singularities each of which looks like a solution of the Yamabe problem on the unit sphere $\mathbb{S}^N$. This is joint work with Monica Musso (University of Bath, UK)