Roberto Araujo (Institute of Mathematics of the Polish Academy of Sciences) – Homogeneous Ricci flows and the dynamical Alekseevskii conjecture
- Date
- @ Leonard Rogers (8.42), 15:00
- Location
- Leonard Rogers (8.42)
- Notes
- Note the unusual room and day
- Speaker
- Roberto Araujo
- Affiliation
- Institute of Mathematics of the Polish Academy of Sciences
- Category
- Geometry and Analysis
Notes: Note the unusual room and day.
A fundamental problem in differential geometry is understanding the constraints that the topology of a manifold imposes on its geometry. In this direction, the dynamical Alekseevskii conjecture states that if the universal cover of a homogeneous space is not contractible, then every homogeneous Ricci flow solution on it has finite extinction time. Böhm proved the conjecture for compact homogeneous spaces.
In this talk, we will consider the problem for noncompact homogeneous spaces. We will show that the conjecture is true for natural families of initial homogeneous metrics satisfying certain compatibility conditions between the Lie algebra structure and the metric. We will also discuss the problem of determining the limit geometries that can be obtained after parabolic rescaling of these solutions, as well as some applications.