##### Department of Mathematics,

University of California San Diego

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### RTG Colloquium

## Morgan Brown

#### University of Miami

## Berkovich geometry and Birational geometry

##### Abstract:

Let $K$ be a field with a valuation $v$. Given a projective variety $X$ over $K$, we can associate an analytification $X^{an}$ with respect to $v$ called the Berkovich space. These spaces appear in various contexts, such as tropical geometry and number theory. More recently there have appeared surprising connections between Berkovich geometry and birational geometry. I will give a brief overview of Berkovich spaces with examples, and describe how the birational geometry of $X$ is reflected in the geometry of the associated Berkovich space.

Host: James McKernan

### March 2, 2016

### 1:00 PM

### AP&M 6402

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