Abstracts

Long time behaviour of ancient homogeneous Ricci flows

Anusha M. Krishnan, Indian Institute of Technology Bombay, Mumbai

A Ricci flow solution (M,g(t)) defined for all negative times, is said to be ancient. On a compact homogeneous space, the Ricci flow restricts to a finite-dimensional dynamical system on the space of left-invariant metrics. We will explain how within this setting, ancient solutions essentially emanate from Einstein metrics, possibly on a lower dimensional space. More precisely, we prove that every ancient homogeneous Ricci flow on a compact manifold admits a blow-down sequence that converges to a gradient shrinking Ricci soliton. This is based on joint work with Francesco Pediconi.