##### Department of Mathematics,

University of California San Diego

****************************

### Math 208: Seminar in Algebraic Geometry

## Dr. Morgan Brown

#### University of Miami

## Birational geometry and Berkovich spaces

##### Abstract:

Berkovich spaces give a formalism for constructing spaces of valuations on varieties over nonarchimedean fields. As such they encode a great deal of information from birational geometry. The most notable invariant is the essential skeleton, a subset of the Berkovich space corresponding to the valuations monomial on strata of a dlt minimal model of 𝑋. Inspired by Mori's conjecture in birational geometry, we conjecture that the essential skeleton is the complement of the images of all transcendental disks, which are analytic objects analogous to families of rational curves. I will present some progress on this conjecture in joint work with Jiachang Xu and Muyuan Zhang.

Host: James McKernan

### June 14, 2024

### 4:00 PM

AP&M 6402

****************************