##### Department of Mathematics,

University of California San Diego

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### Math 258 - Differential Geometry Seminar

## Valentino Tosatti

#### McGill University

## Smooth asymptotics for collapsing Ricci-flat metrics

##### Abstract:

I will discuss the problem of understanding the collapsing behavior of Ricci-flat Kahler metrics on a Calabi-Yau manifold that admits a holomorphic fibration structure, when the Kahler class degenerates to the pullback of a Kahler class from the base. I will present new work with Hans-Joachim Hein where we obtain a priori estimates of all orders for the Ricci-flat metrics away from the singular fibers, as a corollary of a complete asymptotic expansion.

Host: Luca Spolaor

### March 10, 2021

### 10:00 AM

### Zoom link: Meeting ID: 988 8132 1752

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