Stability of 4-dimensional shrinking Ricci solitons

Abstract: Dimension 4 is the next horizon for applications of Ricci flow to topology, where the main goal is to understand the topological operations that Ricci flow generically performs at singular times. Shrinking Ricci solitons model these topological operations, and only the stable ones should arise generically.

I will present recent joint works with Olivier Biquard and Keaton Naff that determine the stability of all of the currently known shrinking Ricci solitons in dimension 4. The arguments use structural features unique to dimension four, in particular self-duality.

algebraic geometrydifferential geometrysymplectic geometry

Audience: researchers in the topic

Geometria em Lisboa (IST)

Series comments: To receive the series announcements, which include the
Zoom access password*, please register in
math.tecnico.ulisboa.pt/seminars/geolis/index.php?action=subscribe#subscribe
*the last announcement for a seminar is sent 5 hours before the seminar.

Geometria em Lisboa video channel: educast.fccn.pt/vod/channels/bu46oyq74