##### Department of Mathematics,

University of California San Diego

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### Food For Thought Seminar

## Henning Hohnhold

#### UCSD

## What is a stack?

##### Abstract:

The goal is to explain what a stack is and why people think they are interesting objects to study. I'll start by saying what people (who want to classify a certain class of mathematical objects, say triangles or elliptic curves or...) expect from a moduli space and why it can easily happen that such a moduli `space' doesn't exist. This is the situation in which stacks get their chance. They are some kind of a generalization of a the notion of a `space', where the meaning of space depends on what you are interested in (for example, in the context of algebraic geometry one might say that stacks are a generalization of the notion of a scheme). I'll then use an example to motivate the axioms appearing in the definition of a stack. Depending on how much time I have I will say what an algebraic stack is and maybe how Deligne and Mumford employed the notion to prove something interesting.

### April 26, 2007

### 11:00 AM

### AP&M B412

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