Title: Smooth asymptotics for collapsing Calabi-Yau metrics
Speaker: Hans Joachim Hein (Mathematisches Institute, Munster)
Date: 07 December 2020
Time: 4:00 pm
Venue: MS teams (team code hiq1jfr)
Yau’s solution of the Calabi conjecture provided the first nontrivial examples of Ricci-flat Riemannian metrics on compact manifolds.
Attempts to understand the degeneration patterns of these metrics in families have revealed many remarkable phenomena over the years.
I will review some aspects of this story and present recent joint work with Valentino Tosatti where we obtain a complete asymptotic expansion
(locally uniformly away from the singular fibers) of Calabi-Yau metrics collapsing along a holomorphic fibration of a fixed compact Calabi-Yau manifold.
This relies on a new analytic method where each additional term of the expansion arises as the obstruction to proving a uniform bound on one additional
derivative of the remainder.