##### Department of Mathematics,

University of California San Diego

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### Advancement to Candidacy

## Shaunak Das

#### UCSD

## Vector Bundles on Perfectoid Spaces

##### Abstract:

Perfectoid spaces were very recently introduced by Scholze and Kedlaya-Liu, independently. These objects provide geometric context to the field-of-norms isomorphism from p-adic Hodge Theory, which relates absolute Galois groups in characteristic 0 and characteristic p. In this talk, I will discuss what perfectoid spaces are, why they are soo hawt right now, and then present some natural questions about their geometry which I am interested in answering.

Advisor: Kiran Kedlaya

### February 9, 2015

### 1:00 PM

### AP&M 6402

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